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Can you solve this integral?
The integral from 0 to a/2 of x^2 (a^2 - x^2)^(-3/2) dx
Details on the method you used would be helpful. Thank you in advance!
1 Answer
- δοτζοLv 79 years agoFavorite Answer
x = a sin(u)
dx = a cos(u) du
∫ x²(a² - x²)^(-3/2) dx = ∫ a²sin²(u)(a²(1 - sin²))^(-3/2) (a cos(u)) du
(a³ a⁻³) ∫ sin²(u)cos(u)cos(u)⁻³ du
∫ tan²(u) du
∫ (sec²(u) - 1) du
That's trivial to integrate. Just change the limits to the u-domain (or back substitute to x) and evaluate.
