Question

Evaluate: `int_-1^1 x^17.cos^4x  dx`

Options

• `oo`

• 1

• – 1

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Answer 1

0

Explanation:

Let f(x) = x¹⁷ cos⁴x

∴ f(– x) = (– x)¹⁷ cos⁴(– x)

= – x¹⁷ cos⁴x

= – f(x)

`\implies` f(x) is an odd function.

So by the property of definite integration.

`int_-a^a f(x)dx` = 0

If f(x) is an odd function.

`\implies int_-1^1 x^17 cos^4x  dx` = 0