1 / | | sin(2*x)*cos(3*x) dx | / 0
Integral(sin(2*x)*cos(3*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:
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:
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:
So, 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:
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:
/ 5 | 3 8*cos (x) | sin(2*x)*cos(3*x) dx = C + 2*cos (x) - --------- | 5 /
2 2*cos(2)*cos(3) 3*sin(2)*sin(3) - - + --------------- + --------------- 5 5 5
=
2 2*cos(2)*cos(3) 3*sin(2)*sin(3) - - + --------------- + --------------- 5 5 5
Use the examples entering the upper and lower limits of integration.