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Homework Statement
I'm trying to solve ##\int\sqrt{a^2 - x^2}##
by using the substitution ##x = asin\theta##
Homework Equations
##x = asin\theta
The Attempt at a Solution
##y = \int\sqrt{a^2 - a^2cos^2\theta}##
##y = a\int\cos\theta##
##y = a^2\int\cos(\theta)^2##
##y = (a^2)/2 * \int1+cos2\theta##
##y = a^2/2 + a^2/4 * sin2\theta\ + C##
##\theta = arcsin(x/a)##
##a^2/2 * arcsin(x/a) + a^2/2 * sin\theta\cos\theta\ + C## Any help would greatly be appreciated.
The answer in the book is ##(a^2/2) * arcsin(x/a) + (x/2) * \sqrt{a^2 - x^2} + C##
EDIT: I figured it out.
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