Questions: ∫ from 0 to π / 2 of 45 sin^2 x cos^3 x dx =

Transcript text: $\int_{0}^{\pi / 2} 45 \sin ^{2} x \cos ^{3} x d x=$

Solution

Step 1: Identify the Integral

The given integral is of the form $\int \sin^{2}(x) \cos^{3}(x) dx$.

Step 2: Apply Integration Techniques

One of the exponents is odd, use the identity $\sin^2(x) + \cos^2(x) = 1$ to simplify the integral.

Step 3: Perform the Integration

The definite integral from 0 to pi/2 is calculated.

$\int \sin^{2}(x) \cos^{3}(x) dx = \frac{2}{15}$ , evaluated from 0 to pi/2, is approximately 0.13.$

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