Mathematics: (1 point) Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^3,y=4x

9000Step-by-step explanation:Harry s loan is initially $9000. This is before t months. His remaining debt will change this....

(1 point) Find the volume of the solid formed by

Ответ:

mianelson367

10.05.2021

Mathematics

(1664π)/7

Step-by-step explanation:

We first need to know the points of intersection of the two functions, y = x³ and y = 4x.

To do this, we equate both functions

x³ = 4x

x³– 4x = 0

x(x² – 4) = 0

x(x – 2)(x + 2) = 0

x = 0, x = 2 and x = –2

Since we are looking for the volume formed by rotating the region inside the FIRST QUADRANT, then the needed points of x are 0 and 2. These are our limits of integration.

The formula for the area of the solid is

$ \int\limits^2_0 {\pi (4x)^3} \, dx -\int\limits^2_0 {\pi (x^3)^3} \, dx$

This gives:

$ \int\limits^2_0 {64\pi x^3} \, dx -\int\limits^2_0 {\pi x^6} \, dx$

On integration, we have

16π(2⁴) – π(2^7)/7

256π – 128π/7

= (1792π – 128π)/7

= (1664π)/7

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(1 point) Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y=x^3,y=4x

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