Suppose you are trying to evaluate the intergral 2x^3dx and you make the substitution u=x^2. The substitution takes one area and converts it to a different one-in this case a trapezoid with vertical sides. Denote by R the region under the first curve from 3 to 3.01 and estimate it's area. Now sketch the region S that the substitution transformed R into and compute its area. Explain how we converted a trall skinny region into a shorter broader one. Especially explain how the du played a role vs. dx.
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