Statement 1: The value of the integral ∫π245π24dx1+tan2x is equal to π12Statement 2: ∫abf(x) dx = ∫abf(a + b − x) dx

Let, I = ∫π245π24dx1 + tan 2x...........(1)Also,I = ∫π245π24tan 2x1 + tan 2x...........(2)By adding (1) and (2), we getStatement-1 is true∵ ∫abf(x) dx = ∫abf(a + b − x) dxIt is fundamental property.Statement-2 is true.

Statement 1: The value of the integral ∫π245π24dx1+tan2x is equal to π12Statement 2: ∫abf(x) dx = ∫abf(a + b − x) dx

Let, I = ∫π245π24dx1 + tan 2x...........(1)Also,I = ∫π245π24tan 2x1 + tan 2x...........(2)By adding (1) and (2), we getStatement-1 is true∵ ∫abf(x) dx = ∫abf(a + b − x) dxIt is fundamental property.Statement-2 is true.

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Statement 1: The value of the integral $\int_{\frac{π}{24}}^{\frac{5 π}{24}} \frac{d x}{1 + \sqrt{\tan 2 x}}$ is equal to $\frac{π}{12}$
Statement 2: $\int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

Statement-1 is true, Statement 2 is true; Statement-2 is a correct explanation for Statement-1

Statement-1 is true; Statement 2 is true; Statement-2 is not a correct explanation for Statement 1.

Statement-1 is true; Statement-2 is false.

Statement-1 is false, Statement-2 is true.

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Let, $I = \int_{\frac{π}{24}}^{\frac{5 π}{24}} \frac{d x}{1 + \sqrt{\tan 2 x}} ........... (1)$

Also,

$I = \int_{\frac{π}{24}}^{\frac{5 π}{24}} \frac{\sqrt{\tan 2 x}}{1 + \sqrt{\tan 2 x}} ........... (2)$

By adding (1) and (2), we get
Statement-1 is true
$∵ \int_{a}^{b} f (x) d x = \int_{a}^{b} f (a + b - x) d x$
It is fundamental property.
Statement-2 is true.