1 / | | / 2 2 \ | |------- - 3*sin (x)| dx | | 2 | | \cos (x) / | / 0
Integral(2/cos(x)^2 - 3*sin(x)^2, (x, 0, 1))
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:
The integral of a constant times a function is the constant times the integral of the function:
Don't know the steps in finding this integral.
But the integral is
So, the result is:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | / 2 2 \ 3*x 3*sin(2*x) 2*sin(x) | |------- - 3*sin (x)| dx = C - --- + ---------- + -------- | | 2 | 2 4 cos(x) | \cos (x) / | /
3 2*sin(1) 3*cos(1)*sin(1) - - + -------- + --------------- 2 cos(1) 2
=
3 2*sin(1) 3*cos(1)*sin(1) - - + -------- + --------------- 2 cos(1) 2
-3/2 + 2*sin(1)/cos(1) + 3*cos(1)*sin(1)/2
Use the examples entering the upper and lower limits of integration.