Sunday

November 23, 2014

November 23, 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

**Answer this Question**

**Related Questions**

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

Calculus - Find the volume of the solid whose base is the region in the xy-plane...

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

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 ...

Calculus - integral 0 to sqrt(3) dx/sqrt(4-x^2) I don't understand why the ...

Calculus - Evaluate the indefinite integral: 8x-x^2. I got this but I the ...

Calculus II - Evaluate using u-substitution: Integral of: 4x(tan(x^2))dx ...