1 / | | sin(x)*cos(3*x) dx | / 0
Integral(sin(x)*cos(3*x), (x, 0, 1))
Rewrite the integrand:
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
There are multiple ways to do this integral.
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:
Rewrite the integrand:
Let .
Then let and substitute :
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:
The integral of is when :
So, the result is:
The result is:
Now substitute back in:
So, the result is:
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:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ 2 | 4 3*cos (x) | sin(x)*cos(3*x) dx = C - cos (x) + --------- | 2 /
1 cos(1)*cos(3) 3*sin(1)*sin(3) - - + ------------- + --------------- 8 8 8
=
1 cos(1)*cos(3) 3*sin(1)*sin(3) - - + ------------- + --------------- 8 8 8
Use the examples entering the upper and lower limits of integration.