Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

JEE Main 20246 AprilMorning Shift

Exam: JEE Main
Year: 2024
Date: 6 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Definite Integration

JEE Main 2024 · 6 April · Morning Shift · Mathematics · Definite Integration

∫_0^ π / 4 ( ^2 x ^2 x)/(( ^3 x+ ^3 x)^2) d x is equal to

\int_0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x

is equal to

Options

A $1 / 6$
B $1 / 3$
C $1 / 12$
D $1 / 9$

Correct answer

A. $1 / 6$

Step-by-step solution

Divide

\mathrm{Nr} \& \mathrm{Dr}

by

\cos \mathrm{x} \int_0^{\pi / 4} \frac{\tan ^2 x \sec ^2 x d x}{\left(1+\tan ^3 x\right)^2} d x

Let

1+\tan ^3

\mathrm{x}=\mathrm{t}

\begin{aligned} & \tan ^2 x \sec ^2 x d x=\frac{d t}{3} \\ & \frac{1}{3} \int_1^2 \frac{\mathrm{dt}}{\mathrm{t}^2}=\frac{1}{6} \end{aligned}

$$

Practice Definite Integration on Quantrex Academy →

More from Definite Integration

The value of the definite integral ∫_ 0 ^ 2 1 3^ (x+3)/(2) \, dx is JEE Advanced 2026 The value of the integral ∫_ 0 ^ 2 x(x^2+x+1) ( x+1 )( x^4+x^2+1 ) \, dx is equal to: JEE Main 2026 If ∫_ π/6 ^ π/4 ( (x-(π)/(3)) (x+(π)/(3))+1)dx = α _e( 3 -1) , then 9α^2 is equal to… JEE Main 2026 Let A = bmatrix 1 & 3 & -1 2 & 1 & α 0 & 1 & -1 bmatrix be a singular matrix. Let f(x) =… JEE Main 2026 Let f: ℝ arrow ℝ be such that f(xy) = f(x)f(y) , for all x, y ∈ ℝ and f(0) ≠ 0 . Let g… JEE Main 2026 The value of the integral ∫ _ -1 ^ 1 ((x^3 + |x| + 1)/(x^2 + 2|x| + 1)) dx is equal to : JEE Main 2026 The value of the integral ∫_ -π/4 ^ π/4 ( 32 ^4 x 1 + e^ x )dx is: JEE Main 2026 Let (2^ 1-a + 2^ 1+a ) , f(a) , (3^a + 3^ -a ) be in A.P. and α be the minimum value of… JEE Main 2026 Let f: [1, ∞) arrow R be a differentiable function defined as f(x) = ∫_1^x f(t)\,dt +… JEE Main 2026 The value of the integral ∫_0^∞ ( _e(x))/(x^2 + 4)\,dx is: JEE Main 2026 The value of the integral ∫_ π/6 ^ π/3 ((4 - ^2 x)/( ^4 x)) dx is: JEE Main 2026 The integral ∫_ 0 ^ 1 ^ -1 (1+x+x^2)dx is equal to: JEE Main 2026 Let f be a twice differentiable function such that f(x)=∫_ 0 ^ x (t-x)dt-∫_ 0 ^ x f(t)… JEE Main 2026 Let ∫_ -2 ^ 2 (| x| + [x x])\,dx = 2(3 - 2) + β , where [·] is the greatest integer… JEE Main 2026 The value of ∫_0^ 20π ( ^4 x + ^4 x) \, dx is equal to: JEE Main 2026 Let [·] denote the greatest integer function. Then the value of ∫_0^3 ( e^x + e^ -x [x]!… JEE Main 2026 Full Definite Integration list Definite Integration JEE Maths PYQs JEE Mathematics PYQs All JEE Main PYQs