Question

Integration problem.

Answer 1

\[\int\limits_{0}^{a} x \sqrt{a^2 - x^2} dx \]

Answer 2

did u try
u = a^2-x^2
?

Answer 3

I didn't, I'm not really sure how to solve it.

Answer 4

oh, try it
u = a^2-x^2
du = ...?

Answer 5

du = 2a - 2x or would it just be du = -2x (if a is just a constant?)

Answer 6

x = a sinx
a^2 - a^2sin^2 x = a^2(1 - sin^2 x) = a^2cos^2 x

that might helps :)

Answer 7

'a' is constant
so,
du = -2x dx
so,
xdx = (-1/2)du
got this?

Answer 8

That makes sense so far.

Answer 9

now change the limits
when x= 0
u =... ?

Answer 10

so is dx = -1/2?

Answer 11

we already got x dx

Answer 12

the question had x dx in it
which we will replace by (-1/2)du

Answer 13

so... do I have \[(-1/2) \int\limits_{0}^{a} x \sqrt{u} du =\]

Answer 14

no..
and we still didn't change the limits

Answer 15

I'm not sure what you're saying I should change.

Answer 16

the limits
from 0 to a for 'x'
now we need limits for 'u'
u =a^2-x^2
when x=0, what does u equal ?