1 / | | 3 2 | sin (x)*cos (x)*1 dx | / 0
Integral(sin(x)^3*cos(x)^2*1, (x, 0, 1))
Rewrite the integrand:
There are multiple ways to do this integral.
Let .
Then let and substitute :
Integrate term-by-term:
The integral of is when :
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 result is:
Now substitute back in:
Rewrite the integrand:
Integrate term-by-term:
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 is when :
So, the result is:
Now substitute back in:
So, the result is:
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 is when :
So, the result is:
Now substitute back in:
The result is:
Rewrite the integrand:
Integrate term-by-term:
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 is when :
So, the result is:
Now substitute back in:
So, the result is:
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 is when :
So, the result is:
Now substitute back in:
The result is:
Add the constant of integration:
The answer is:
/ | 3 5 | 3 2 cos (x) cos (x) | sin (x)*cos (x)*1 dx = C - ------- + ------- | 3 5 /
3 5 2 cos (1) cos (1) -- - ------- + ------- 15 3 5
=
3 5 2 cos (1) cos (1) -- - ------- + ------- 15 3 5
Use the examples entering the upper and lower limits of integration.