3 years ago

I really need help thia is my last chance to get a good grade in math-

Mathematics

1 answer:

romanna [79]3 years ago

8 0

Answer:

Step-by-step explanation:

bsahaahaaana

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Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the curves about the given

Fed [463]

See attachment for one such shell. The volume is given by the sum of infinitely many thin shells like this, each with radius $x$ and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given $x$ , i.e. $8e^x-8e^{-x}$ .

The volume is then

$2\pi\displaystyle\int_0^1x\left(8e^x-8e^{-x}\right)\,\mathrm dx=16\pi\int xe^x(e^{2x}-1)\,\mathrm dx=\dfrac{32\pi}9(e^3-4)\approx179.677$