JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q10

MathematicsSingle correct+4 / -1Question 10 of 90

The value of the integral $\displaystyle\int_{-2}^2\frac{\left|x^3+x\right|}{\left(e^{x|x|}+1\right)}dx$ is equal to :

5e^2

3e^{-2}

Answer and worked solution

Official answer: D

Symmetry. $|x^3+x|$ is even and $x|x|$ is odd, so $\displaystyle\int_{-2}^2\frac{g(x)}{1+e^{x|x|}}dx=\int_0^2g(x)\,dx$ .

Value. $\displaystyle\int_0^2(x^3+x)\,dx=4+2=6$ .

(D)

Topics:Properties of definite integrals

JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 10