Hey,guys I need help

Advanced Placement (AP)

1 answer:

garik1379 [7]3 years ago

6 0

A. Growing industrialization, more small farmers

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AP CALC QUESTION!! WILL MARK BRAINLIEST (TWO QUESTIONS)

kodGreya [7K]

1. Using washers, the volume is given by the integral

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$=\boxed{\displaystyle\pi\int_1^{e^2}(20+4\ln x-(\ln x)^2)\,\mathrm dx}$

We're using washers whose centers depend on the value of $x$ , hence we integrate with respect to

2. The area of the given region is given by the integral

$\displaystyle\int_0^2\sin^{-1}\frac x2\,\mathrm dx$

To compute the integral, first consider the substitution $u=\frac x2$ , or $2u=x$ so that $2\,\mathrm du=\mathrm dx$ . Then $x\to0\implies u\to0$ and $x\to2\implies u\to1$ , so the integral is equivalently