Primitive of inverse sin (1 Viewer)

[youngminii]

Fitzpatrick 3u pg 156 Q 47.
Prove that d/dx(xasinx) = asinx + x/(sqrt(1 - x^2)). Hence find the primitive of asinx and show that the integral sign thingo (upper bound 1/2, lower bound 0) asinxdx = pi/12 + sqrt3/2 - 1.

That looks messy.. Anyways, there's another question where my answer disagreed with Fitzy's answers:
Pg 155 Q 39.
Sketch the graph of y = 2sin(pix/4) for 0<=x<=2 and x = 2sin(piy/2) for 0<=y<=2 and find the area of the region enclosed by the curves.
I got 4 - pi/16 but the answers say pi/16 - 4.

Thansk a lot.
(asin = inverse sin)

 

[lolokay]

 

[youngminii]

Oh. Didn't know how to integrate x/(sqrt(1-x^2)) bit.. Haha thanks heaps.
Do you just use substitution to integrate it? Bah, I better re-do integration.

 

[lolokay]

yeah, use substitution/reverse chain rule