Question

6. Let R be the region in the xy-plane bounded by the curves $y = x^3 - 4x$ and y = -3x where $x \ge 0$. a) Sketch the curves and label their intersection(s) for $x \ge 0$. b) Find the area of R. c) Find the volume of the solid of revolution obtained by rotating R about the x-axis. Express your answer in terms of $\pi$ as needed. d) Find the volume of the solid of revolution obtained by rotating R about the y-axis. Express your answer in terms of $\pi$ as needed.

          6.
Let R be the region in the xy-plane bounded by the curves $y = x^3 - 4x$ and
y = -3x where $x \ge 0$.
a) Sketch the curves and label their intersection(s) for $x \ge 0$.
b) Find the area of R.
c) Find the volume of the solid of revolution obtained by rotating R about the
x-axis. Express your answer in terms of $\pi$ as needed.
d) Find the volume of the solid of revolution obtained by rotating R about the
y-axis. Express your answer in terms of $\pi$ as needed.

6.
Let R be the region in the xy-plane bounded by the curves y = x^3 - 4x and
y = -3x where x ≥ 0.
a) Sketch the curves and label their intersection(s) for x ≥ 0.
b) Find the area of R.
c) Find the volume of the solid of revolution obtained by rotating R about the
x-axis. Express your answer in terms of π as needed.
d) Find the volume of the solid of revolution obtained by rotating R about the
y-axis. Express your answer in terms of π as needed.

Added by Ethan F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carson Merrill

08/22/2022

Step 1

The two curves are y=x^(3)-4x and y=-3x. To find their intersection, we set them equal to each other: x^(3)-4x = -3x x^(3)-x = 0 x(x^(2)-1) = 0 x(x-1)(x+1) = 0 So the intersection points are at x=0, x=1, and x=-1. However, since x>=0, the only intersection point Show more…

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Let R be the region in the xy-plane bounded by the curves y=x^(3)-4x and y=-3x where x>=0. a) Sketch the curves and label their intersection(s) for x>=0. b) Find the area of R. c) Find the volume of the solid of revolution obtained by rotating R about the x-axis. Express your answer in terms of pi as needed. d) Find the volume of the solid of revolution obtained by rotating R about the y-axis. Express your answer in terms of pi as needed. 6. Let R be the region in the xy-plane bounded by the curves y = x3 -- 4x and y = --3x where x 0. a) Sketch the curves and label their intersection(s) for x 0. b) Find the area of R. c) Find the volume of the solid of revolution obtained by rotating R about the x-axis. Express your answer in terms of T as needed. (p Find the volume of the solid of revolution obtained by rotating R about the y-axis. Express your answer in terms of t as needed.