POST_GRBEK_SMALL_pi ------------------- 2 / | | e*cos(x)*sin(x)*1 dx | / 0
Integral(E*cos(x)*sin(x)*1, (x, 0, POST_GRBEK_SMALL_pi/2))
The integral of a constant times a function is the constant times the integral of the function:
There are multiple ways to do this integral.
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:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ 2 | e*cos (x) | e*cos(x)*sin(x)*1 dx = C - --------- | 2 /
2/POST_GRBEK_SMALL_pi\ e*sin |-------------------| \ 2 / --------------------------- 2
=
2/POST_GRBEK_SMALL_pi\ e*sin |-------------------| \ 2 / --------------------------- 2
Use the examples entering the upper and lower limits of integration.