Question

integration sin theta cos^4 theta
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Answer 1

Step-by-step explanation:

We have,

$\int \limits^{ \frac{\pi}{2} }_{0} \sin( \theta) \cos^{4} ( \theta)d \theta$

$\int \limits^{ \frac{\pi}{2} }_{0} \cos^{3} ( \theta) .\sin( \theta) \cos ( \theta)d \theta$

$= - \frac{1}{2} \int \limits^{ \frac{\pi}{2} }_{0} ( \cos^{2} ( \theta))^{ \frac{3}{2} } . (- 2\sin( \theta) \cos ( \theta))d \theta$

$let \: \: \cos^{2} ( \theta) = t \\ \implies - 2 \sin( \theta) \cos( \theta) d \theta = dt$

$= - \frac{1}{2} \int \limits^{ 0 }_{1} ( t)^{ \frac{3}{2} } dt$

$= \frac{1}{2} \int \limits^{1 }_{0} ( t)^{ \frac{3}{2} } dt$

$= \frac{2}{5 \times 2} .[t ^{ \frac{5}{2} }]^{1}_{0}$

$= \frac{1}{5} (1 - 0)$

$= \frac{1}{5}$

Answer 2

Step-by-step explanation:

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