Chapter 5: Q 40. (page 452)

Solve the following integral.
$\int \sin^{2} x \cos^{3} x d x$

Short Answer

Expert verified

Answer is $\frac{\sin^{3} x}{3} - \frac{\sin^{5} x}{5} + C$

Step by step solution

Step 1. Given information

An integral is $\int \sin^{2} x \cos^{3} x d x$

Step 2. Explanation

$\int \sin^{2} x \cos^{3} x d x = \int (1 - \sin^{2} x) \sin^{2} x \cos x d x$

Let $u = \sin x$

$\begin{array}{rcl} \int \sin^{2} x \cos^{3} x d x & = & \int u^{2} (1 - u^{2}) d u \\ = & \int u^{2} - u^{4} d u \\ = & \frac{u^{3}}{3} - \frac{u^{5}}{5} + C \\ = & \frac{\sin^{3} x}{3} - \frac{\sin^{5} x}{5} + C \end{array}$

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Solve the following integral.
$\int \sin^{2} x \cos^{3} x d x$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Solve the following integral.∫sin2xcos3xdx

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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Solve the following integral.
$\int \sin^{2} x \cos^{3} x d x$