Posted by **Marissa** on Monday, September 8, 2008 at 3:55am.

How can I solve the integral of x^3√(9-x^2) dx using trigonometric substitution? ?

∫ x^3√(9-x^2) dx

So then I know that

x = 3sinθ

dx = 3cosθdθ

When I substitute, it becomes

∫ (3sinθ)^3 * √(9-(3sinθ)^2) * 3cosθdθ

= ∫ (27sin^3θ * (3 - 3sinθ)* 3cosθdθ

Is there any way to furter simplify this before I solve it? And if there isn't, how would I go about solving it?

## Answer this Question

## Related Questions

- Calculus AP - hi again im really need help TextBook: James Stewart:Essential ...
- Precalc/Trig - Sorry there are quite a few problems, but I just need to know if ...
- Pre-Calculus - If θ represents an angle such that sin2θ = tanθ - ...
- Trig - Prove (3cosθ-4sinθ)^2+(4cosθ+3sinθ)^2=25
- Math - Find all solution of the trigonometric equation 3cosθ-√3=0 for...
- Trig - Given that tan θ = - (√3/8) and θ is in QII, find the ...
- trig - An object Is propelled upward at an angle θ, 45° < θ<90...
- Integral Calculus - Solve using Integration by Substitution : ∫√x2-...
- math trigono - 1. If tanθ = –√3 , what is the value of cot ? 2. ...
- trigonometry help please :( - 2) Simplify √-1-4/5-√-1 A.-1/24+19/24i...

More Related Questions