Friday

April 25, 2014

April 25, 2014

Posted by **Sammy** on Sunday, February 10, 2013 at 7:19pm.

Evaluate the integral xsqrt(100-x^2dx) for the interval (0,10)

- Calculus -
**Steve**, Sunday, February 10, 2013 at 7:26pmlet x = 10sinθ. then

dx = 10cosθ dθ

√(100-x^2) = √(100-100sin^2θ = 10√(1-sin^2θ) = 10cosθ

The integral then becomes

∫(10cosθ)(10cosθ dθ) = 100∫cos^2 θ dθ

which I'm sure you can do.

The limits of integration then become

0<=x<=10 --> 0 <= θ <= π/2

**Related Questions**

Calculus III - I'm supposed to find the expression 'y', when (x^2+100)y'=23 When...

calculus - consider the function f(x) = e^x(sinNx) on the interval [0,1] where N...

calculus - consider the function f(x) = e^x(sinNx) on the interval [0,1] where N...

Calculus - Use integration by parts to evaluate the integral xsqrt(2x+6)dx.

Calculus integral - evaluate the integral: integral from -pi/4 to 0 for the ...

math,correction - simplify: sqrt ((7)/(100)) my work: 7 = 1sqrt (7) 100= 10 sqrt...

Calculus - Evaluate: integral x^3/[sqrt*(x^2+100)]dx can someone tell me what ...

Calculus - Evaluate: integral x^3/[sqrt*(x^2+100)]dx can someone tell me what ...

improper integral - can any one explain how to evaluate this improper integral i...

Calculus - Evaluate the integral below by interpreting it in terms of areas. In ...