Someone argues: "To evaluate

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Calculus of change and accumulation · Calculus of change and accumulation

Mathematical Methods for Physics, Ch Accumulation: integration and the techniques that make it possible

Problem

Someone argues: "To evaluate ∫132x ex2 dx\displaystyle\int_1^3 2x\,e^{x^2}\,\mathrm{d}x, let u=x2u = x^2, so du=2x dx\mathrm{d}u = 2x\,\mathrm{d}x. Then ∫132x ex2 dx=∫13eu du=[eu]13=e3−e≈17.37."\int_1^3 2x\,e^{x^2}\,\mathrm{d}x = \int_1^3 e^u\,\mathrm{d}u = \left[e^u\right]_1^3 = e^3 - e \approx 17.37." ((a)) Find the error in this working. ((b)) Give the correct value of the integral, and check it by differentiating the antiderivative used back to the original integrand.

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