Cynthia Bell

2021-12-26

Given a curve having an equation of ${y}^{2}=4x$ .

a) Compute the area bounded by the curve and the line$y=4$ and $x=0$ .

b) How far is the centroid of the curve bounded by the line$y=4$ and $x=0$ from the x-axis.

c) What is the volume generated by this curve if it is revolved about the x-axis.

a) Compute the area bounded by the curve and the line

b) How far is the centroid of the curve bounded by the line

c) What is the volume generated by this curve if it is revolved about the x-axis.

turtletalk75

Beginner2021-12-27Added 29 answers

Given: -

To Find: - Area bounded by the curve

Area

Deufemiak7

Beginner2021-12-28Added 34 answers

b) To Find: - How For centroid of centroid

X-axis

i.e. we need to find y coordinute of centroid

$y=\frac{1}{\text{Area}}{\int}_{x=a}^{x=b}\frac{1}{2}(\left({f\left(x\right)}^{2}\right)-\left({g\left(x\right)}^{2}\right)\text{dx}$

$=\frac{1}{\frac{16}{3}}{\int}_{0}^{4}\frac{1}{2}[{4}^{2}-{\left(2\sqrt[()]{x}\right)}^{2}]\text{dx}$

$=\frac{3}{32}{\int}_{0}^{4}(16-4x)\text{dx}$

$=\frac{3\times 4}{32}{\int}_{0}^{4}(4-x)\text{dx}$

$=\frac{3}{8}[4x-\frac{{x}^{2}}{2}]=\frac{3}{8}\left(8\right)=3$

$$ Centroid of curve is 3 from x-axis

X-axis

i.e. we need to find y coordinute of centroid

karton

Expert2022-01-09Added 613 answers

c) To Find: - Value generated by come f revolved about x-axis:

Volume of Solid revolved about the x-axis is given by

whose y=f(x) is upper come f y=g(x) lower curve.

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