Question

integrate (x^2)*(2-x)^.5
from 0 to 4

Answer 1

I got
-64/15
or -4.26666

Answer 2

\[\int\limits_{0}^{4} x^2(2-x)^{1/2} dx\]

Answer 3

had to do u-sub, right?

Answer 4

what do you get if you let x = 4 in the function you are integrating?

Answer 5

I don't follow. That's what I did, after u-substitution,

Answer 6

you are integrating a function, let's call it f(x), where: \[f(x) = x^2 \ (2−x)^\frac{1}{2}\]over the region 0≤x≤4.

so you are calculating the area under f(x) over region 0≤x≤4.

have you plotted f(x) ??

and what happens to f(x) when x > 2 ??

Answer 7

No plotting neccissary, it's just an integral.