Area under the Region

[Lime]

Find the area of the region under the curve

f(x) = x (4 - x^2)^1/2

between a and b.

a = 0, b = 2

 

[galactus]

\(\displaystyle \L\\\int_{0}^{2}x\sqrt{4-x^{2}}dx\)

Try the substitution:

\(\displaystyle \L\\u=4-x^{2}; \;\ du=-2xdx\)

 

[Lime]

Where do you get -2x dx?

 

[galactus]

I am sorry, but if you can't see that, then you're not ready for these sorts of problems and you should see your instructor.