0 / | | / 1 \ | |- ----- + cos(x)| dx | | ___ | | \ \/ x / | / pi -- 2
Integral(-1/sqrt(x) + cos(x), (x, pi/2, 0))
Integrate term-by-term:
The integral of cosine is sine:
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 a constant is the constant times the variable of integration:
So, the result is:
Now substitute back in:
So, the result is:
The result is:
Add the constant of integration:
The answer is:
/ | | / 1 \ ___ | |- ----- + cos(x)| dx = C - 2*\/ x + sin(x) | | ___ | | \ \/ x / | /
___ ____ -1 + \/ 2 *\/ pi
=
___ ____ -1 + \/ 2 *\/ pi
-1 + sqrt(2)*sqrt(pi)
Use the examples entering the upper and lower limits of integration.