# How do you evaluate the integral of #int (sin^4x)dx#?

Definitively the fastest way to do that, is to use euler formula

expand with binomial theorem

so

which is

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

To evaluate the integral of ( \int \sin^4(x) , dx ), you can use the reduction formula for powers of sine.

First, rewrite ( \sin^4(x) ) as ( (\sin^2(x))^2 ). Then, apply the half-angle identity ( \sin^2(x) = \frac{1 - \cos(2x)}{2} ) to obtain ( \left(\frac{1 - \cos(2x)}{2}\right)^2 ).

Expand this expression and integrate each term separately. After integration, substitute ( u = \cos(2x) ) and proceed with the calculation. Finally, revert to the original variable ( x ) to obtain the final result.

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

To evaluate the integral of ∫sin^4(x)dx, you can use the double angle identity for sine, which states that sin^2(x) = (1 - cos(2x))/2. By substituting this identity into sin^4(x), you get (1 - cos(2x))^2/4. Then, expand the squared term and integrate each part separately. The integral simplifies to (3x/8) - (sin(4x)/8) + (sin(2x)/4) + C, where C is the constant of integration.

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

To evaluate the integral of (\int \sin^4(x) , dx), you can use the reduction formula or trigonometric identities. One approach is to rewrite (\sin^4(x)) using the power-reducing identity: (\sin^2(x) = \frac{1 - \cos(2x)}{2}). Then, use a double angle formula to further simplify and integrate. Alternatively, you can use trigonometric identities to express (\sin^4(x)) in terms of (\cos(2x)), and then integrate. Both methods will lead to the same result.

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