Sketch the region enclosed by the given curves. Decide whether
to integrate with respect to x or y. Draw a
typical approximating rectangle.
y =
2/x, y =
2/x2, x =
7
And also find the area
Sketch the region enclosed by the given curves. Decide whether
to integrate with respect to x or y. Draw a typical approximating
rectangle. y = 2 + 2 sqrt(x) , y = (6 + x) / 3
1.Sketch the region enclosed by the graphs of each of the
following curves, and determine the area of the region enclosed by
the graphs of the functions:
y=x^2
y=4x-x^2
2. Find the area between the graph of and the x axis
on the interval [-3, 1].
Consider the region R enclosed between the curves y = 2 /x and y
= 1, between x = 1 and x = 2.
Calculate the volume of the solid obtained by revolving R about
the x-axis,
(a) using cylindrical shells;
(b) using washers
FIND THE CENTROID:
a. of the region enclosed between the curves y=x1/2 ,
y=1, y=2 and the y-axis.
b. of the 1st quadrant area bounded by the curve
y=4-x2
c. of the region bounded by the curve y=x3 and
x=y2
Sketch the region in the first quadrant enclosed by y=2/x ,
y=3x, and y=1/3x. Decide whether to integrate with respect to x or
y. Then find the area of the region.
Area =
Find the area of the region enclosed between y=4sin(x) and
y=2cos(x) from x=0 to x=0.4π
Hint: Notice that this region consists of two parts.
a. Find the volume of the solid obtained by rotating the region
enclosed by the curves y = 4 x^2 , y = 5 − x^2 about the line y =
11
b. Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis.
y = 2sqt (x), y=x, about x=-20.
Please leave your answer in fraction if
possble