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