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Travka [436]
3 years ago
6

Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x^4 , and the lines x = 1 a

nd x = -1 about the x-axis.
Mathematics
1 answer:
Marysya12 [62]3 years ago
8 0

Answer:

Let's define A as the area given by the integral:

\int\limits^1_{-1} {3x^4} \, dx

Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1

To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)

where pi = 3.14

First, let's solve the integral:

\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}

Then the volume of the solid is just:

V = (6/5)*2*3.14 = 7.536

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(c) what do you think the enteries of Ik are?

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\delta I_{ij}=1\quad if\quad i=j\\\delta I_{ij}=0\quad if\quad i\ne j\\

Any power of 1 is equal to 1 so kth power of 1 is also 1. According to this Ik=I

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