1 / | | __________ | / 2 | \/ 9 - 3*x dx | / 0
Integral(sqrt(9 - 3*x^2), (x, 0, 1))
SqrtQuadraticRule(a=9, b=0, c=-3, context=sqrt(9 - 3*x**2), symbol=x)
Now simplify:
Add the constant of integration:
The answer is:
/ / ___\ | __________ ___ |x*\/ 3 | | __________ / 2 3*\/ 3 *asin|-------| | / 2 x*\/ 9 - 3*x \ 3 / | \/ 9 - 3*x dx = C + --------------- + --------------------- | 2 2 /
/ ___\ ___ |\/ 3 | ___ 3*\/ 3 *asin|-----| \/ 6 \ 3 / ----- + ------------------- 2 2
=
/ ___\ ___ |\/ 3 | ___ 3*\/ 3 *asin|-----| \/ 6 \ 3 / ----- + ------------------- 2 2
Use the examples entering the upper and lower limits of integration.