Integration q again ~ >.<" (1 Viewer)

[jesshika]

im having trouble integrating this definite integral questin from 24g q 17

pi
2sin@ cos@ dx
0

 

[nike33]

probably better ways, but

u = cos^2 @
du = -2cos@sin@ d@

sqr(u) = cos@

sub that in i think u will get it

 

[CM_Tutor]

Let u = cos@. Then du = -sin@ d@. At @ = 0, u = 1, and at @ = pi, u = -1

So, we have int (from 1 to -1) -2 *u² du = [2u³ / 3] from -1 to 1
= (2 / 3) *[1³ - (-1)³] = 4 / 3