1 / | | /sin(2*x) 2 \ | |-------- + sin (x)| dx | | ___ | | \ \/ 1 / | / 0
Integral(sin(2*x)/sqrt(1) + sin(x)^2, (x, 0, 1))
Integrate term-by-term:
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:
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ | | /sin(2*x) 2 \ x cos(2*x) sin(2*x) | |-------- + sin (x)| dx = C + - - -------- - -------- | | ___ | 2 2 4 | \ \/ 1 / | /
cos(2) cos(1)*sin(1) 1 - ------ - ------------- 2 2
=
cos(2) cos(1)*sin(1) 1 - ------ - ------------- 2 2
1 - cos(2)/2 - cos(1)*sin(1)/2
Use the examples entering the upper and lower limits of integration.