1 / | | ______________ | \/ 2*sin(x) - 1 *cos(x) dx | / 0
Integral(sqrt(2*sin(x) - 1)*cos(x), (x, 0, 1))
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:
Now simplify:
Add the constant of integration:
The answer is:
/ | 3/2 | ______________ (2*sin(x) - 1) | \/ 2*sin(x) - 1 *cos(x) dx = C + ----------------- | 3 /
_______________ _______________ \/ -1 + 2*sin(1) I 2*\/ -1 + 2*sin(1) *sin(1) - ----------------- + - + -------------------------- 3 3 3
=
_______________ _______________ \/ -1 + 2*sin(1) I 2*\/ -1 + 2*sin(1) *sin(1) - ----------------- + - + -------------------------- 3 3 3
-sqrt(-1 + 2*sin(1))/3 + i/3 + 2*sqrt(-1 + 2*sin(1))*sin(1)/3
(0.188144900963713 + 0.333094621053717j)
(0.188144900963713 + 0.333094621053717j)
Use the examples entering the upper and lower limits of integration.