Mathematics

Mathematics

Problem

Which of the following definite integrals gives the length of a smooth planar curve described explicitly as x=g(y)x=g(y) for c≤y≤dc\le y\le d? a) ∫cd1+(dydx)2 dy\displaystyle\int_{c}^{d} \sqrt{1+\left(\dfrac{dy}{dx}\right)^{2}}\,dy b) ∫cd1+(dxdy)2 dy\displaystyle\int_{c}^{d} \sqrt{1+\left(\dfrac{dx}{dy}\right)^{2}}\,dy c) ∫cd1+(dxdy)2 dx\displaystyle\int_{c}^{d} \sqrt{1+\left(\dfrac{dx}{dy}\right)^{2}}\,dx d) ∫cd(dxdy)2 dy\displaystyle\int_{c}^{d} \sqrt{\left(\dfrac{dx}{dy}\right)^{2}}\,dy

Browse the problem library