How do you find the integral of #int sin^5(x)cos^8(x) dx#?
By signing up, you agree to our Terms of Service and Privacy Policy
To find the integral of (\int \sin^5(x)\cos^8(x) , dx), you can use trigonometric identities and integration by parts. Here's how:
- Start by using the identity (\sin^2(x) = 1 - \cos^2(x)) to rewrite (\sin^5(x)) as ((1 - \cos^2(x))^2\sin(x)).
- Expand ((1 - \cos^2(x))^2) using the binomial theorem.
- Now you have an integral involving powers of (\sin(x)) and (\cos(x)), which you can integrate using integration by parts.
- Let (u = \cos(x)) and (dv = \sin^4(x)\cos^4(x) , dx), then differentiate (u) to find (du) and integrate (dv) to find (v).
- Apply integration by parts formula: (\int u , dv = uv - \int v , du).
- Substitute the values of (u), (du), (dv), and (v) into the integration by parts formula and evaluate the integral.
- Repeat the process if necessary until you obtain an expression that can be easily integrated.
Following these steps will lead you to the solution of the integral (\int \sin^5(x)\cos^8(x) , dx).
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.
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