Question

Evaluate the following integral

Answer 1

\[I=\int\limits_{0}^{\pi/2} \sin(2x) \cos^2(x) dx\]

Answer 2

I have no idea how to go about this one

Answer 3

my guess is to rewrite \(\sin(2x)=2\sin(x)\cos(x)\) and then use one of those reduction formulas or else a u - sub

Answer 4

Yes I seen that too but I don't quite understand what happens to the square?

Answer 5

probably u - sub for this one
\[2\int \sin(x)\cos^3(x)dx\] use \(u=\cos(x)\)

Answer 6

Oh so is sin(2x) an identity of 2sin(x)cos(x)? :

Answer 7

yes that is the gimmick here

Answer 8

http://www.math.com/tables/trig/identities.htm

Answer 9

Ah perfect I can go from here, thanks!

Answer 10

then it is straight forward right?

Answer 11

oh good
yw

Answer 12

Would the answer be 1/2

Answer 13

\[\int\limits_{0}^{\pi/2} \sin(2x) \cos^2(x) dx\]
\[\int\limits_{0}^{\pi/2} 2\sin(x) \cos^3(x) dx\]
\[-\left.\frac12cos^4(x)~\right|_{0}^{90}\]
at 90 cos = 0 sooo, yeah. 0 - (-1/2) = 1/2