Understanding the Locus of a Vector: Homework Question & Solution

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Homework Statement


What is the locus of the head of R = (t+1)i + (t^2 + 2t +3)j


Homework Equations





The Attempt at a Solution


I have no idea what a locus of a vector is? Is it like a moving point or something?
Thanks
 
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It's the curve in the xy plane that the head of the vector passes through. Yes, find the curve of the 'moving point'. Write x=t+1 and y=t^2+2t+3, eliminate the t and see if you recognize the resulting xy equation.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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