# How do you evaluate the definite integral #int sin^(5)x * cos^(20)x dx# from [0,pi/2]?

By signing up, you agree to our Terms of Service and Privacy Policy

To evaluate the definite integral ∫ sin^5(x) * cos^20(x) dx from 0 to π/2, you can use the substitution u = sin(x), then du = cos(x) dx. This transforms the integral into ∫ u^5 * (1 - u^2)^10 du. You can then expand (1 - u^2)^10 using the binomial theorem, integrate the resulting polynomial, and evaluate it from 0 to 1.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7