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Choose the correct option.
Evaluate: ∫₋₁¹ x¹⁷cos⁴ x dx
Evaluate: $\int_{-1}^1 x^{17}\cos^4 x\,dx$
- (a)$\infty$
- (b)$1$
- (c)$-1$
- (d)$0$
Answer
Answer
Correct option: (d)
Answer: (d) $0$
Let $g(x) = x^{17}\cos^4 x$. Then $g(-x) = -g(x)$, so $g$ is odd.
For an odd function $\int_{-a}^{a} g(x)\,dx = 0$.