1 / | | 3 | sin (x)*sin(2*x) dx | / 0
Integral(sin(x)^3*sin(2*x), (x, 0, 1))
There are multiple ways to do this integral.
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 is when :
Now substitute back in:
So, the result is:
Rewrite the integrand:
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 is when :
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ | 5 | 3 2*sin (x) | sin (x)*sin(2*x) dx = C + --------- | 5 /
3 3 2 2 2*sin (1)*cos(2) 2*cos (1)*sin(2) 4*cos (1)*cos(2)*sin(1) sin (1)*cos(1)*sin(2) - ---------------- + ---------------- - ----------------------- - --------------------- 5 5 5 5
=
3 3 2 2 2*sin (1)*cos(2) 2*cos (1)*sin(2) 4*cos (1)*cos(2)*sin(1) sin (1)*cos(1)*sin(2) - ---------------- + ---------------- - ----------------------- - --------------------- 5 5 5 5
-2*sin(1)^3*cos(2)/5 + 2*cos(1)^3*sin(2)/5 - 4*cos(1)^2*cos(2)*sin(1)/5 - sin(1)^2*cos(1)*sin(2)/5
Use the examples entering the upper and lower limits of integration.