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INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS2 Marks
Question
Write a value of $\int\cos^4\text{x }\sin\text{x}\text{ dx}$
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Answer

Let $\text{I}=\int\cos^4\text{x }\sin\text{x}\text{ dx}$
Let $\cos\text{x}=\text{t}$
$-\sin\text{x dx}=\text{dt}$
$\text{I}=-\int\text{t}^{4}\text{ dt}$
$=-\frac{\text{t}^5}{5}+\text{C}$
$\text{I}=\frac{\cos^5\text{x}}{5}+\text{C}$

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