{"id":2010,"date":"2021-12-23T15:57:54","date_gmt":"2021-12-23T10:27:54","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=2010"},"modified":"2023-04-27T12:48:08","modified_gmt":"2023-04-27T07:18:08","slug":"ncert-solutions-for-class-12-maths-chapter-7-integrals-ex-7-1-exercise-7-1","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-1\/","title":{"rendered":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals (Ex 7.1) Exercise 7.1"},"content":{"rendered":"<p><span data-contrast=\"auto\">NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.1 have been created by Infinity Learn&#8217;s experienced teachers to help you enhance your math and analytical skills. The solutions are written in simple steps to help you comprehend the subject better. You will also be given reference notes to help you grasp the basic notion of the topic. The solutions can be downloaded in pdf format from Infinity Learn&#8217;s official website. If you still have questions about the concepts, you can contact one of the instructor teams listed on the website. The introduction of Integral is the first step in <strong><span style=\"color: #0000ff;\">NCERT Solutions for Class 12 Maths<\/span><\/strong> Chapter 7 Exercise 7.1. The two types of Integrals, Definite Integral and Indefinite Integral are discussed in this chapter. The fundamental theorem of Calculus is the relationship between these two forms of integrals. Integration as an inverse process of differentiation, geometrical interpretation of indefinite integral, features of indefinite integral, and comparison of differentiation and integration are some of the other topics covered in this chapter. Here are some quick snippets of theory to help you solve the antiderivatives and integrals in Exercise 7.1.<\/span><\/p>\n<p>&nbsp;<\/p>\n\n\t\t<div class=\"download-pdf-container\">\n\t\t\t<span class=\"title\">Do you need help with your Homework? 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wpcf7-validates-as-required wpcf7-validates-as-number\" aria-required=\"true\" aria-invalid=\"false\" \/><\/span><\/p>\n<p><span style=\"display:none;\"><span class=\"wpcf7-form-control-wrap current-page-url\"><input type=\"text\" name=\"current-page-url\" value=\"https:\/\/_:443\/surge\/wp-json\/wp\/v2\/posts\/2010\" size=\"40\" class=\"wpcf7-form-control wpcf7dtx-dynamictext wpcf7-dynamictext\" aria-invalid=\"false\" \/><\/span><\/span><\/p>\n<style>.wpcf7-list-item{margin: 0 0.5em 0 0!important;}<\/style>\n<p class=\"title\" style=\"color: #6e6e6e;font-size:14px;font-weight:400;text-decoration: un;\"><span class=\"wpcf7-form-control-wrap acceptance-agreement\"><span class=\"wpcf7-form-control wpcf7-acceptance\"><span class=\"wpcf7-list-item\"><input type=\"checkbox\" name=\"acceptance-agreement\" value=\"1\" aria-invalid=\"false\" checked=\"checked\" \/><\/span><\/span><\/span> I agree to the <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/terms\" style=\"text-decoration: underline;\">terms and conditions<\/a> and <a target=\"_blank\" href=\"https:\/\/infinitylearn.com\/privacy\" style=\"text-decoration: underline;\">privacy policy<\/a>.<\/p>\n<p><input type=\"button\" style=\"cursor:pointer;width:auto;\" class=\"il_otp_submit\" value=\"Get OTP\" onclick=\"sendCF7OTP(this, otp_phone.value, user_name.value)\"><\/p>\n<div class=\"form-submit-btn-div\" style=\"display:none;\">\n<input type=\"submit\" value=\"Download PDF\" class=\"wpcf7-form-control has-spinner wpcf7-submit download-pdf-submit\" \/>\n<\/div>\n<\/div>\n<div class=\"wpcf7-response-output\" aria-hidden=\"true\"><\/div><\/form><\/div>\n\t\t\t\t\t<span class=\"pdf-link hidden\" data-pdf=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-7.1.pdf\"><\/span>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t<div class=\"bg-overlay\"><\/div>\n\t\t<\/div>\n\t\t<a href=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/Exercise-7.1.pdf\" class=\"pdfemb-viewer\" style=\"\" data-width=\"max\" data-height=\"max\" data-mobile-width=\"0\"  data-scrollbar=\"both\" data-download=\"off\" data-tracking=\"on\" data-newwindow=\"on\" data-pagetextbox=\"off\" data-scrolltotop=\"on\" data-startzoom=\"100\" data-startfpzoom=\"100\" data-toolbar=\"top\" data-toolbar-fixed=\"on\">Exercise 7.1<br\/><\/a>\n<p>&nbsp;<\/p>\n<p><span style=\"color: #0000ff;\"><b>NCERT Solutions For Exercise 7.1 Maths Class 12<\/b>  <\/span><\/p>\n<p><span style=\"color: #0000ff;\"><b>Introduction<\/b> <\/span><\/p>\n<p><span data-contrast=\"auto\">Calculus is a discipline of mathematics that was developed independently in the latter part of the 17th century by Sir Isaac Newton and G.W Leibnitz (a German mathematician). The subject of calculus can be separated into two parts:<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ol>\n<li><span data-contrast=\"auto\">Calculus of Differences<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">Calculus of Integrals<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ol>\n<p><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><span data-contrast=\"auto\">Differential Calculus is concerned with determining the rate of change of a quantity such as a displacement, velocity, or acceleration, often known as finding the derivative of the quantity.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Integral Calculus aids in the determination of a quantity when the rate of change is known, implying that integration is the inverse of differentiation. This is why the anti-derivative of a function is called the integral of the function.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span style=\"color: #0000ff;\"><b>Integral Calculus Is Divided Into Two Types Once More.<\/b> <\/span><\/p>\n<ol>\n<li><span data-contrast=\"auto\">Integral indefinite<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<li><span data-contrast=\"auto\">Integral Definite<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ol>\n<p><span data-contrast=\"auto\">Definite Integral is used to discover the area limited by a curve given particular conditions, while Indefinite Integral is used to identify a function if its derivatives are known.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\"><strong>Note:<\/strong> Previously, calculating the area of basic forms with straight lines, such as a triangle, rectangle, or trapezium, was simple, but calculating the area under curved lines was difficult. This problem was solved with the use of integral calculus. Integral is widely used in a variety of domains, including engineering, physics, economics, and biology.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span data-contrast=\"auto\">Infinity Learn presents several integration approaches that can assist you in solving the <span style=\"color: #0000ff;\"><strong><a style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/ncert-solutions\/\" target=\"_blank\" rel=\"noopener\">NCERT Solutions<\/a><\/strong><\/span>.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p aria-level=\"3\"><b><span data-contrast=\"none\">Why Should You Download Ex 7.1 Class 12 Maths Solutions?<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559738&quot;:320,&quot;335559739&quot;:80,&quot;335559740&quot;:331}\"> <\/span><\/p>\n<p aria-level=\"3\"><span data-contrast=\"auto\">The following are the reasons why you should obtain the Class 12 Maths Chapter 7 Exercise 7.1 solution.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"1\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><b><span data-contrast=\"auto\">Dispel Any Doubts<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">The first exercise does not need to be completed by the entire class. You can do it on your own and have reservations about it. After you&#8217;ve written down your questions, look at the Ex 7.1 Class 12 Maths NCERT Solutions to see how the experts came up with the solutions. Compare your results to those of the professionals to see where you may improve. As a result, you will be able to effortlessly clear your worries and progress to the next level without difficulty.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"2\" aria-setsize=\"-1\" data-aria-posinset=\"2\" data-aria-level=\"1\"><b><span data-contrast=\"auto\">At Its Finest, Convenience<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">There&#8217;s no need to be concerned when you have the Class 12 Chapter 7 Maths solution on hand. It is accessible offline and can be referred to at any time. Don&#8217;t waste time waiting for your mentors to come up with a solution. Take advantage of the answer and Learn how to tackle integral problems from the start.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<ul>\n<li data-leveltext=\"\u25cf\" data-font=\"\" data-listid=\"5\" aria-setsize=\"-1\" data-aria-posinset=\"1\" data-aria-level=\"1\"><b><span data-contrast=\"auto\">Creating A Foundation<\/span><\/b><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559685&quot;:720,&quot;335559740&quot;:276,&quot;335559991&quot;:360}\"> <\/span><\/li>\n<\/ul>\n<p><span data-contrast=\"auto\">As previously said, laying a foundation in integration concepts is essential for the future. You will not only do well on the board exam, but you will also pass the entrance exams. Use Exercise 7.1 Maths Class 12 Solutions to prepare your knowledge base for this.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span style=\"color: #0000ff;\"><strong>FAQ:<\/strong> <\/span><\/p>\n<ol>\n<li><span style=\"color: #ff0000;\">Can you explain the distinction between definite and indefinite integrals?<\/span><\/li>\n<li><span style=\"color: #ff0000;\">What exactly do you mean when you say differential calculus?<\/span><\/li>\n<li><span style=\"color: #ff0000;\">How does Infinity Learn&#8217;s NCERT Solutions assist students to prepare for exams?<\/span><\/li>\n<\/ol>\n<p><span style=\"color: #0000ff;\">Q. Can you explain the distinction between definite and indefinite integrals?<\/span><\/p>\n<p><span data-contrast=\"auto\"><span style=\"color: #ff0000;\">Ans. <\/span>The indefinite integral is used to identify a function if its derivative is known, whereas the definite integral is used to calculate the area circumscribed by a curve under particular conditions.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span style=\"color: #0000ff;\">Q. What exactly do you mean when you say differential calculus?<\/span><\/p>\n<p><span data-contrast=\"auto\"><span style=\"color: #ff0000;\">Ans.<\/span> Differential Calculus is concerned with determining the rate of change of a quantity such as a displacement, velocity, or acceleration, often known as finding the derivative of the quantity.<\/span><span data-ccp-props=\"{&quot;201341983&quot;:0,&quot;335551550&quot;:6,&quot;335551620&quot;:6,&quot;335559740&quot;:276}\"> <\/span><\/p>\n<p><span style=\"color: #0000ff;\">Q. How does Infinity Learn&#8217;s NCERT Solutions assist students to prepare for exams?<\/span><\/p>\n<p><span data-contrast=\"auto\"><span style=\"color: #ff0000;\">Ans.<\/span> Infinity Learn&#8217;s NCERT Solutions will undoubtedly strengthen your analytical and mathematical abilities. For a better comprehension of the solutions, the solutions are presented step by step according to the CBSE board&#8217;s most recent syllabus. There are plenty of practice worksheets to aid you in your revision. Solving the NCERT Solutions will increase your self-assurance and help you prepare for the tests.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 12 Maths Chapter 7 Exercise 7.1 have been created by Infinity Learn&#8217;s experienced teachers to help [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"exercise 7.1 class 12 maths","_yoast_wpseo_title":"NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.1","_yoast_wpseo_metadesc":"Free NCERT Solutions for Class 12 Maths Chapter 7 - Integrals solved by Expert Teachers as per NCERT (CBSE) Book guidelines.","custom_permalink":"study-materials\/ncert-solutions\/class-12\/maths\/chapter-7-integrals-exercise-7-1\/"},"categories":[19,31],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 12 Maths Chapter 7 Integrals Exercise 7.1<\/title>\n<meta name=\"description\" content=\"Free NCERT Solutions for Class 12 Maths Chapter 7 - 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