Question

Let X be the region bounded by y=x and y=x^2.

Sketch the region X and find the area. Explain

Answer #1

let R be the region bounded by the curves x = y^2 and x=2y-y^2.
sketch the region R and express the area R as an iterated integral.
(do not need to evaluate integral)

The region is bounded by y=2−x^2 and y=x. (a) Sketch the region.
(b) Find the area of the region. (c) Use the method of cylindrical
shells to set up, but do not evaluate, an integral for the volume
of the solid obtained by rotating the region about the line x = −3.
(d) Use the disk or washer method to set up, but do not evaluate,
an integral for the volume of the solid obtained by rotating the
region about...

Sketch the region bounded by the graphs of the given equations.
y = 2^x, y = 2^-x, y = 0, x = −2, and x = 2 . Find the area of that
region.
EXACT ANSWER ONLY. A DECIMAL ANSWER WILL BE COUNTED INCORRECT.

Sketch the region bounded by the given curves. y = 3 sin x, y =
ex, x = 0, x = π/2 Find the area of the region.

Let X be the region bounded by y=x and y=x^2.
Find the volume of the solid that is made when X is revolved
about the y-axis. Find it in two different methods, include a
diagram for each method, and explain.

Let R be the region bounded by the curves y = x, y = x+ 2, x =
0, and x = 4. Find the volume of the solid generated when R is
revolved about the x-axis. In addition, include a carefully labeled
sketch as well as a typical approximating disk/washer.

Let A be the region bounded by the graphs y = 1 √ x , y = 0, x =
9, and x = 16.
• Write an expression for the area of A.
• Find the area of A.
• Find the vertical line x = c that cuts A’s area exactly in
half.

Find the area of the region bounded by the curves x+y^2= 2 and
x+y=0

Sketch the region enclosed by x = 56 − y^ 2 and x = − y . Then
find the area of the region.

a.) Let S be the solid obtained by rotating the region bounded
by the curves y=x(x−1)^2 and y=0 about the y-axis. If you sketch
the given region, you'll see that it can be awkward to find the
volume V of S by slicing (the disk/washer method). Use cylindrical
shells to find V
b.) Consider the curve defined by the equation xy=12. Set up an
integral to find the length of curve from x=a to x=b. Enter the
integrand below

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