Question
Evaluate the following integrals.$$\int \sin ^{2} x \cos ^{2} x d x$$
Step 1
The power-reduction identity for $\sin^2x$ and $\cos^2x$ is $\sin^2x\cos^2x = \frac{1}{4}\sin^2(2x)$. So, we can rewrite the integral as: $$\int \sin ^{2} x \cos ^{2} x d x = \frac{1}{4}\int \sin^2(2x) dx$$ Show more…
Show all steps
Your feedback will help us improve your experience
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Evaluate the integrals. $$\int\left(\cos ^{2} x+\sin ^{2} x\right) d x$$
Integration Techniques
Trigonometric Techniques of Integration
Evaluate the following integrals. $$\int \frac{\sin x}{\cos ^{2} x+\cos x} d x$$
Integration Strategies
Evaluate the following integrals. $$\int x \cos ^{2}\left(x^{2}\right) d x$$
Integration
Substitution Rule
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD