pi -- 6 / | | 2 | 6*cos (x)*sin(x) dx | / pi -- 2
Integral((6*cos(x)^2)*sin(x), (x, pi/2, pi/6))
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | | 2 3 | 6*cos (x)*sin(x) dx = C - 2*cos (x) | /
___ -3*\/ 3 -------- 4
=
___ -3*\/ 3 -------- 4
-3*sqrt(3)/4
Use the examples entering the upper and lower limits of integration.