x - 2 / | | 2*cos(3*x) dx | / 0
Integral(2*cos(3*x), (x, 0, x/2))
The integral of a constant times a function is the constant times the integral of the function:
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 cosine is sine:
So, the result is:
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ | 2*sin(3*x) | 2*cos(3*x) dx = C + ---------- | 3 /
/3*x\ 2*sin|---| \ 2 / ---------- 3
=
/3*x\ 2*sin|---| \ 2 / ---------- 3
2*sin(3*x/2)/3
Use the examples entering the upper and lower limits of integration.