• anonymous
Check my work on this please? :-) Surface integral for the parametric equations x = 4 + te$$^t$$, y = (t$$^2$$ + 1)e$$^t$$, 0 ≤ t ≤ 3 Reference: Surface Area = $$\large\int\limits_{a}^{b} 2\pi\ y\ ds$$ ds for parametric = $$\large\sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt$$ So... $S.A. = \large\int\limits_{a}^{b} 2\pi\ ((t^2+1)e^t) \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2}\ dt$ $$dx = te^t\ dt$$ $$\large\frac{dx}{dt} = te^t$$ $$dy = (t^2+1)e^t+e^t(2t)\ dt$$ $$\large\frac{dy}{dt} = e^t(t^2+2t+1)$$ $$\large\frac{dy}{dt} = e^t(t+1)^2$$
Mathematics

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