# Calculus with Analytical Geometry II## Integral Evaluation ExampleEvaluate the following definite integral:\[\int_{0}^{\frac{\pi}{2}} (\sin x)^2 (\cos x)^4 \, dx\]### Options for the Solution1. \(\frac{\pi}{16}\)2. \(\frac{\pi}{8}\)3. \(\frac{\pi}{32}\)4. \(\frac{\pi}{64}\)In this example, you are required to determine the value of the definite integral, which involves trigonometric functions raised to a power. The process may involve trigonometric identities and integration techniques, such as substitution or integration by parts.### Tip for Solving:Consider using trigonometric identities to simplify the powers of sine and cosine before integrating. For example, identities such as \(\sin^2 x = \frac{1 - \cos(2x)}{2}\) and \(\cos^2 x = \frac{1 + \cos(2x)}{2}\) might be helpful.### Further Explanation:In approaching problems like this one, break down the integral into more manageable parts using algebraic manipulation and trigonometric identities. This often simplifies the computation and leads to more straightforward integration.

Name: # Calculus with Analytical Geometry II## Integral Evaluation ExampleE
Uploaded: 2024-03-20T06:46:42.000Z
Channel: Bartleby
Description: # Calculus with Analytical Geometry II## Integral Evaluation ExampleEvaluate the following definite integral:\[\int_{0}^{\frac{\pi}{2}} (\sin x)^2 (\cos x)^4 \, dx\]### Options for the Solution1. \(\frac{\pi}{16}\)2. \(\frac{\pi}{8}\)3. \(\frac{\pi}