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If $f (x) = \int_{0}^{x} \sin^{8} t d t,$ then $f (x + π)$ equals

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detailed solution

Correct option is C

f(x+π)=∫0x+π sin8⁡tdt=∫0π sin8⁡tdt+∫πx+π sin8⁡tdt=f(x)+∫0x sin8⁡(π−u)du=f(π)+f(x).

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If f(x)=∫0x sin8⁡tdt,then f(x+π) equals

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Ready to Test Your Skills?

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If $f (x) = \int_{0}^{x} \sin^{8} t d t,$ then $f (x + π)$ equals