p - 4 / | | / 2 2 \ | \cos (x) - sin (x)/ dx | / 0
Integral(cos(x)^2 - sin(x)^2, (x, 0, p/4))
Integrate term-by-term:
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 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:
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 cosine is sine:
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 cosine is sine:
So, the result is:
Now substitute back in:
So, the result is:
The integral of a constant is the constant times the variable of integration:
The result is:
The result is:
Add the constant of integration:
The answer is:
/ | | / 2 2 \ sin(2*x) | \cos (x) - sin (x)/ dx = C + -------- | 2 /
/p\ /p\ cos|-|*sin|-| \4/ \4/
=
/p\ /p\ cos|-|*sin|-| \4/ \4/
cos(p/4)*sin(p/4)
Use the examples entering the upper and lower limits of integration.