How to find the length of parabola?I know that we can find length id the parabola using integral $(1+(\dfrac{dy}{dx})^2)^\dfrac{1}{2}$.But when I was trying to expand that I am unable to end up with finite no of terms.
About the length of parabola
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calculus
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1I think its better to type your question , and tell us what you tried ! – 2017-02-11
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0see here http://planetmath.org/arclengthofparabola i hope this will help you – 2017-02-11
1 Answers
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Hint
Considering $$y=a+b x+c x^2\implies y'=b+2cx$$ you then need to compute between bounds $$\int_{x_1}^{x_2} \sqrt{1+(b+2cx)^2}\,dx$$ Change variable $$b+2c x=t\implies x=\frac{t-b}{2 c}\implies dx=\frac{dt}{2 c}$$ and the antiderivative becomes $$I=\int \sqrt{1+(b+2cx)^2}\,dx=\frac{1}{2 c}\int \sqrt{1+t^2}\,dt$$
I am sure that you can take it from here.