Question

integral of sqrt(1+(1/2)x^2-(1/2)x^(-2)^2)? I'm pretty sure in involves trig substitution, not so sure how though.

Answer 1

Can you please clarify the (1/2)x^(-2)^2 term?

Answer 2

\[\int\limits_{1/2}^{1} \sqrt{1+((1/2)x^2-(1/2)x ^{-2})^2}\]
Sorry about that, does that help?

Answer 3

Dont wory about trig. Try working down the fraction

Answer 4

\[\large =\int\limits_{\frac{1}{2}}^{1}\sqrt{\frac{ (x^4+1)^2 }{ 4x^4 }}\]
\[\large =\int\limits_{\frac{1}{2}}^{1}\frac{(x^4+1)}{2x^2}\]
\[\large =\int\limits_{\frac{1}{2}}^{1}\frac{1}{2}x^2+\frac{1}{2}x^{-2}\]
\[\large =\frac{1}{6}x^3-\frac{1}{2}x^{-1}\]
\[\large =[\frac{1}{6}(1)^3-\frac{1}{2}(1)]-[\frac{1}{6}(\frac{1}{8})-\frac{1}{2}(2)]\]