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nika2105 [10]
2 years ago
10

Write and evaluate the definite integral that represents the volume of the solid formed by revolving the region about the x-axis

. y= -x+2
Mathematics
1 answer:
Romashka [77]2 years ago
7 0

The definite integral of the given function will be \pi(\dfrac{1304}{27}).

<h3>What is integration?</h3>

Integration is defined as the summing up of the small parts to find the total value.The given function y = -x +2 will be integrated as follows:-

The limits are given as a = 0 and b = 2.

The integration will be done as:-

V = \pi\int_0^2\pi(y^2)dx\\\\\\V = \pi\int _0^2(\pi(-x+2)^2dx\\\\\\V = \pi\int _0^2(x^2+16+8x)dx\\\\\\V=\pi [ (\dfrac{x^3}{3}+16x+\dfrac{8x^2}{2}]_0^2\\\\\\V = \pi[(\dfrac{2^3}{3^3}+(16\times 2) + 8\dfrac{2)^2}{2}]-0\\\\\\V = \dfrac{1304}{27}\pi

Therefore definite integral of the given function will be \pi(\dfrac{1304}{27}).

To know more about integration follow

brainly.com/question/15993715

#SPJ1

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So the sum is x + (x - 1) + (x - 2) + (x - 3) + (x - 4) = -5

Now solve for x:

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5x - 10 = -5

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So the largest number is 1.

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Answer:

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