JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q9

MathematicsSingle correct+4 / -1Question 9 of 90

$\displaystyle\int_0^{20\pi}\left(|\sin x|+|\cos x|\right)^2dx$ is equal to

10(\pi+4)

10(\pi+2)

20(\pi-2)

20(\pi+2)

Answer and worked solution

Official answer: D

Square. $(|\sin x|+|\cos x|)^2=1+|\sin2x|$ .

Integrate. $|\sin2x|$ has period $\frac\pi2$ with integral 1 over each period, and $[0,20\pi]$ holds 40 periods: $20\pi+40=20(\pi+2)$ .

(D)

Topics:Properties of definite integrals

JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 9