Search for: if f(x)=x+∫01 t(x+t)f(t)dt, then the value of 232f(0) is equal to__. if f(x)=x+∫01 t(x+t)f(t)dt, then the value of 232f(0) is equal to__. Fill Out the Form for Expert Academic Guidance!l Grade ---Class 1Class 2Class 3Class 4Class 5Class 6Class 7Class 8Class 9Class 10Class 11Class 12 Target Exam JEENEETCBSE +91 Preferred time slot for the call ---9 am10 am11 am12 pm1 pm2 pm3 pm4 pm5 pm6 pm7 pm8pm9 pm10pm Please indicate your interest Live ClassesBooksTest SeriesSelf Learning Language ---EnglishHindiMarathiTamilTeluguMalayalam Are you a Sri Chaitanya student? NoYes Verify OTP Code (required) I agree to the terms and conditions and privacy policy. Solution:f(x)=x+x∫01 tf(t)dt+∫01 t2f(t)dt∴ f(x)=x(1+A)+B whereA=∫01 tf(t)dt and B=∫01 t2f(t)dtNow, A=∫01 t[t(1+A)+B]dt=t33(1+A)01+B2t201=1+A3+B2or 4A−3B=2 (1)Again, B=∫01 t2[t(1+A)+B]dt=t4(1+A)4+Bt3301==1+A4+B3or 8B−3A=3 (2)Solving equations (1) and (2), we have B=1823=f(0). Related content CBSE Class 7 English Honeycomb Chapter 2 A Gift of Chappals MCQ Questions with Answers Top Career Option and Courses after 12th 2024: Arts, Commerce & Science Students CBSE Class 7 English MCQ Questions with Answers CBSE Class 12 English Lost Spring MCQ with Answers Heron’s Formula Class 9 Worksheet Maths Chapter 12 CBSE Class 12 English The Last Lesson MCQ with Answers Was NEET 2024 Paper Leaked? Check NTA Official Press Release CBSE Class 10 English Chapter 1 Worksheets -A Letter to God Disaster Management Project for Class 9 ICSE ISC Topper List 2024, Check ISC Class 12 Topper List for Science, Commerce, Arts