The value of $\int\limits_{-\pi/2}^{\pi/2}(x^5+x^3\cos x)dx$ is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
Integral: $\displaystyle \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} (x^5 + x^3\cos x)\,dx$
$x^5$ is an odd function → integral over symmetric limits = $0$.
$x^3$ is odd and $\cos x$ is even → product $x^3\cos x$ is odd → integral over symmetric limits = $0$.
Total integral = $0 + 0 = 0$
The value of the integral is $0$.