Find the volume (in units3) generated when the region between the curves is rotated around the given axis. x = y2 and y = x rota

Question

2 years ago

9

ted around the line y = 3

1 answer:

densk [106] · Answer 1 · 2023-08-07T03:08:55+03:00

The volume (in units3) is generated when the region between the curves is rotated around the given axis.is mathematically given as

$v=\frac{5 \pi}{6}$

<h3>What is the volume (in units3) generated when the region between the curves is rotated around the given axis. ?</h3>

The region is bound by

x=y^2

y=x

y=3

Where

y=√x

Generally, the equation for Washer Method is mathematically given as

$v=\int ^1_0 \pi ((outer curve)^2-(inner Curve)^2) dx$

Therefore

v= $\int_{0}^{1} \pi(-7 x)+\pi x^{2}+6 \pi \sqrt{x} d x$

v= $\frac{5 \pi}{6}$

In conclusion, The result can be shown in multiple forms

Exact Form:

$\frac{5 \pi}{6}$

Decimal Form:

2.61799387