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Question about where to start this trig substitution integral

  • Thread starter vande060
  • Start date
  • #1
186
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Homework Statement



∫ x^2√(a^2 - x^2) dx evaluate integral from 0 to a







Homework Equations





The Attempt at a Solution



so i know the format of this problem requires the substitution of asinϑ -π/2 ≤ ϑ ≤ π/2 , but i dont know how to change the bounds of the integral after the substitution of ϑ. i just nedd help with this point the rest of the problem shouldnt be an issue
 

Answers and Replies

  • #2
52
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You're substituting x = a sin (t) so plug your limits into x then solve for t.
Ex:
0 = a sin(t) -> 0 = sin(t) -> arcsin(0) = t -> t = 0.

for upper boundary plug in x = a you get:

a = a sin(t) -> 1 = sin(t) -> arcsin(1) = t -> pi/2
 

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