# Math - Trig Substitution

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?

1. 👍 0
2. 👎 0
3. 👁 46
1. ∫ 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

BUT √(9-(3sinθ)^2) = 3 √ (1-sin^2)θ
1 - sin^2 = cos^2

= ∫ (27sin^3θ * (3 - 3 COS θ )* 3cosθdθ

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### Calculus 2

Evalute the integral of x/(x^2+4)dx using u-substitution and then trigonometric substitution. I did this and got (1/2)ln(x^2+4)+C using u-substitution and x^2+4+C using trigonometric substitution. What did I do wrong??? thank you

asked by Heather on October 10, 2012
2. ### Math

(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in

asked by Jack on February 7, 2017
3. ### Question on Integration

(i) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using trigonometric substitution. (ii) Evaluate integral [ x^3 / (x^2 + 4)^2 ] using regular substitution. (iii) Use a right triangle to check that indeed both answers you obtained in

asked by Murphy on February 7, 2017
4. ### Calculus

I have two questions, because I'm preparing for a math test on monday. 1. Use the fundamental theorem of calculus to find the derivative: (d/dt) the integral over [0, cos t] of (3/5-(u^2))du I have a feeling I will be able to find

asked by Jennifer on May 9, 2009
5. ### Calculus

For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x^2)/(sqrt(7x^2+4))dx dx x=?

asked by Salman on December 14, 2009
6. ### Calculus

For the following integral find an appropriate trigonometric substitution of the form x=f(t) to simplify the integral. INT((4x^2-3)^1.5) dx x=?

asked by Salman on December 10, 2009
7. ### Calculus

For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT (x)/(sqrt(-191-8x^2+80x))dx x=?

asked by Salman on December 14, 2009
8. ### Calculus

For the following integral find an appropriate TRIGONOMETRIC SUBSTITUTION of the form x=f(t) to simplify the integral. INT x(sqrt(8x^2-64x+120))dx x=?

asked by Salman on December 14, 2009
9. ### calculus

For trigonometric substitution to solve the above integral, fill in the blanks below using the picture of the triangle given. integral (x^3)/(sqrt(25+9x^2)) dx / l / l / l / l / l / l / l / l / l side A / l / l --------- side B

asked by Chiara on April 19, 2011
10. ### calculus

Suppose R is the rectangle 1

asked by Bryant on March 18, 2012
11. ### Calculus 2

find the integral of x/(x^2+4)dx using trigonometric substitution.

asked by Heather on October 10, 2012

More Similar Questions