∫_-1^1 xcos^4x dx is equal to

The correct answer is Option (1) → 0

Let \(f(x) = x\cos^{4}x\). Then

    \(f(-x) = (-x)\cos^{4}(-x) = -x\cos^{4}x = -f(x)\)

So f is an odd function. For an odd function on a symmetric interval,

    \( \displaystyle \int_{-a}^{a} f(x)\,dx = 0 \)

Hence the integral is 0.