Question

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.

Answer #1

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

The curves x = sin y and y = (x − 1)^2 + π/2 along with the line
x = 0 create a bounded region, D, in x ≥ 0, 0 ≤ y ≤ 3. (a) Sketch D
and identify a type I region D1 and a type II region D2 such that D
= D1∪D2. (b) Find the area of D using the regions from a)

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified line.
a) y = sin x − 2(x − 1)2 + 2(π − 1)2 , y =
0, about the x axis.

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.

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)

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

Find the volume V of the solid obtained by rotating the
region bounded by the given curves about the specified line.
y = 2 + sec(x),
−π
3
≤ x ≤
π
3
, y = 4; about
y = 2
V =
Sketch the region.
Sketch the solid, and a typical disk or washer.

Let X be the region bounded by y=x and y=x^2.
Sketch the region X and find the area. Explain

Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
y=0,y=cos(4x), x= π/8, x=0 about the axis y=−2

Calculate the area of the region bounded by the curves x=3-y^2 and
x=y+1

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