1 / | | ________ | / 2 | \/ 1 - r *r dr | / 0
Integral(sqrt(1 - r^2)*r, (r, 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:
Add the constant of integration:
The answer is:
/ | 3/2 | ________ / 2\ | / 2 \1 - r / | \/ 1 - r *r dr = C - ----------- | 3 /
Use the examples entering the upper and lower limits of integration.