1 / | | 2 | sin (2*x) dx | / 0
Integral(sin(2*x)^2, (x, 0, 1))
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
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:
The result is:
Add the constant of integration:
The answer is:
/ | | 2 x sin(4*x) | sin (2*x) dx = C + - - -------- | 2 8 /
1 cos(2)*sin(2) - - ------------- 2 4
=
1 cos(2)*sin(2) - - ------------- 2 4
1/2 - cos(2)*sin(2)/4
Use the examples entering the upper and lower limits of integration.