Evaluate the integral: ∫√(64−x^2) dx?
Evaluate the integral:
∫√(64−x^2) dx on [-5,5]
Hint: Use the "multiply by 1" trick with integration by parts
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Evaluate the integral:
∫√(64−x^2) dx on [-5,5]
Hint: Use the "multiply by 1" trick with integration by parts
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Verified answer
x = 8sin(u)
dx = 8cos(u) du
∫√(64−x^2) dx on [-5,5]
= ∫8cos(u) 8cos(u) du on [arcsin(-5/8), arcsin(5/8)]
= 32 ∫(1+cos2u) du
= 32[u + (1/2)sin(2u)] on [arcsin(-5/8), arcsin(5/8)]
= 32[2arcsin(5/8) + 2(5/8)(sqrt(39)/8]
= 64arcsin(5/8) + 5sqrt(39)