Evaluate a definite integral

Asked Jun 01 '14 at 13:11

Active Jun 01 '14 at 13:11

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Evaluate: $$\int_{0}^{1} x^2\sqrt{(kx^2-1)(kx^2-1+t)}\, dx$$

where k and t are constants.

Can you help me?

asked Jun 01 '14 at 13:11

user154564

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This looks like a job for integration under the integral sign. – David H Jun 01 '14 at 13:17
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Also, what have you tried? – Alice Ryhl Jun 01 '14 at 13:23
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i tried $$kx^2-1=z$$ but nothing...what do you suggest? Have you tried to solve it on your own? – user154564 Jun 01 '14 at 13:26
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Instead of trying $kx^2-1=z$ try $z^2$ – Chinny84 Jun 01 '14 at 13:30
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Have you put a space between x and k? – user154564 Jun 01 '14 at 13:35
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I have solved the indefinite integral using mathematica: http://i.imgur.com/lHBkdmC.png input: Integrate[x^2*Sqrt[(k x^2 - 1) (k x^2 - 1 + t)], x] – Alice Ryhl Jun 01 '14 at 13:38
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This is the final result http://i.imgur.com/eyB0hhE.png – Alice Ryhl Jun 01 '14 at 13:42
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@user154564 The result posted is fairly simple as far as elliptic integrals go. Have you encountered elliptic integrals before? – David H Jun 01 '14 at 13:51

0 Answers0