JEE Main 2022 · 29 Jul · Shift 1 · Mathematics Q6

MathematicsSingle correct+4 / -1Question 6 of 90

The integral $\displaystyle\int_0^{\pi/2}\frac1{3+2\sin x+\cos x}\,dx$ is equal to :

\tan^{-1}(2)

\tan^{-1}(2)-\dfrac\pi4

\dfrac12\tan^{-1}(2)-\dfrac\pi8

\dfrac12

Answer and worked solution

Official answer: B

Substitute $t=\tan\frac x2$ : $\displaystyle\int_0^1\frac{2\,dt}{2t^2+4t+4}=\int_0^1\frac{dt}{(t+1)^2+1}=\tan^{-1}2-\frac\pi4$ .

(B)

Topics:Properties of definite integrals Substitution

JEE Main 2022 · 29 Jul · Shift 1, Mathematics question 6