Question

Consider the curve y = e sin x for π /6 ≤ x ≤ π /3 . Set up the integrals (without evaluating) that represent

1. The area of the surface generated by revolving the curve about the x-axis.

2. The area of the surface generated by revolving the curve about the y-axis.

Answer #1

Consider the parametric equations below.
x = t sin(t), y = t
cos(t), 0 ≤ t ≤ π/3
Set up an integral that represents the area of the surface
obtained by rotating the given curve about the x-axis.
Use your calculator to find the surface area correct to four
decimal places

1. Find the area between the curve f(x)=sin^3(x)cos^2(x) and y=0
from 0 ≤ x ≤ π
2. Find the surface area of the function f(x)=x^3/6 + 1/2x from
1≤ x ≤ 2 when rotated about the x-axis.

Consider the region R bounded by y = sinx, y = −sinx , from x =
0, to x=π/2.
(1) Set up the integral for the volume of the solid obtained by
revolving the region R around
x = −π/2
(a) Using the disk/washer method.
(b) Using the shell method.
(2) Find the volume by evaluating one of these integrals.

Let B be the region bounded by the part of the curve y = sin x,
0 ≤ x ≤ π, and the x-axis. Express (do not evaluate) the volume of
the solid obtained by rotating the region B about the y-axis as
definite integrals
a) using the cylindrical shell method
b) using the disk method

Section 2 Problem 4:
a)Find the area of the surface obtained by rotating the
curvex=1/3((y^2)+2)^(3/2), 1<=y<=2, about the x-axis
b)Find the area of the surface generated by revolving the given
curve about the y-axis. x=sqrt(25-y^2), -4<=y<=4

Consider the region S enclosed by the graphs of y=x^3-6^2+9x and
y=x/2 . Determine which solid has the greater volume, and by how
much: (a) The solid generated by revolving S about the x-axis; (b)
The solid generated by revolving S about the line y=4.

Find the area of the surface generated by revolving the curve x
= ?square root 4y − y2, 1 ≤ y ≤ 2, about y-axis.

Sketch the region enclosed by y = sin ( π /3 x ) and y =( − 2
/3) x + 2 . Then find the area of the region.

Consider the plane region R bounded by the curve y = x − x 2 and
the x-axis. Set up, but do not evaluate, an integral to find the
volume of the solid generated by rotating R about the line x =
−1

Find the exact area of the surface obtained by rotating the
curve about the x -axis.
y = sin π x/ 5 , 0 ≤ x ≤ 5

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 11 minutes ago

asked 19 minutes ago

asked 27 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago