Given the function $c(t)=(t, t, t^2)$ what is its arclength from $1 \le t \le 2$?
I find the derivative and its norm, but am stuck at how to solve the integral:
$$\int\sqrt{ax^2 + b} dx$$
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what kind of function is $c'(t)$? i find the notation very strange, is it a parametrized vector? why first two coordinates coincide? – tortue Oct 06 '19 at 19:51
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@pointguard0 my apologies I accidentally added a derivative where it was not supposed to be, I've updated my answer – grahamcracker1234 Oct 06 '19 at 19:55
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This question might be what you are looking for – Varun Vejalla Oct 06 '19 at 20:16
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What is $a,b$, are they in $\mathbb{R}^{\ge0}$ or just in $\mathbb{R}$ – Ethan Oct 06 '19 at 20:19
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In any table of integrals or symbol-manipulation program: $$\frac{1}{2} x \sqrt{a x^2+b}+\frac{b \log \left(\sqrt{a} \sqrt{a x^2+b}+a x\right)}{2 \sqrt{a}}$$ – David G. Stork Oct 06 '19 at 20:33
