25-26 Find the length of the arc of the curve from point P to point Q. 25. y=1/2x^2, P(-1, 1/2), Q(1, 1/2) sqrt(2)+ln(1+sqrt(2)) y' = x integral sqrt(1+x^2) integral from -1 to 1 sqrt(1+x^2) dx tan theta = x dx = sec^2 theta d theta integral from -1 to 1 sqrt(1+tan^2 theta) * sec^2 theta d theta integral from -1 to 1 sec theta * sec^2 theta d theta integral u v' = uv - integral u' v u = sec theta, v = tan theta du = sec theta tan theta, dv = sec^2 theta sec theta tan theta - integral tan theta * sec theta tan theta d theta sec theta tan theta - integral tan^2 theta sec theta d theta
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Step 1:** Given integral: $\int e^{\theta} \, d\theta$ ** Show more…
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I got stuck on the integration by parts, it seems like the integration will go on forever if the two parts are both trig functions. I’m actually not sure if I’m even doing it right. Can you please show me how to solve this.
Gopesh V.
I'm not sure if I am doing this correctly. Is it suppose to be integration by parts? Also the integration by parts seems like it will go on forever since both parts are trig functions. Can you please explain showing all work and not just plugging into some formula in the back of the book? Thank you.
Suzanne W.
Can someone explain how to solve this please? Also explain what to do when it is integration by parts but with trig functions? It seems like the integration will go on forever if it is using trig functions.
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