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
Let R be the region enclosed by the x-axis, the y-axis, the line
x = 2 , and the curve ? = 2?? +3?
(1) Find the area of R by setting up and evaluating the
integral.
(2) Write, but do not evaluate, the volume of the solid
generated by revolving R around
the y-axis
(3) Write, but do not evaluate the volume of the solid generated
by revolving R around
the x-axis
(4) Write, but do not evaluate the...
Consider the region R, which is bounded by the
curves y=3x and x=y(4−y).
(a) Set up, but DO NOT SOLVE, an integral to find the area of
the region RR.
(b) Set up, but DO NOT SOLVE, an integral to find the volume of
the solid resulting from revolving the region RRaround the
xx-axis.
(c) Set up, but DO NOT SOLVE, an integral to find the volume of
the solid resulting from revolving the region RRaround the line
x=−5x=−5.
1. Consider the region bounded by the graph of y^2 = r^2
−x^2
(a) When this region is rotated about the x-axis a sphere of
radius r is generated. Use integration to find its volume V (b) Use
integration to find the surface area of such a sphere
2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60]
(
3. Consider the graph of y = x^3 . Compute the surface area of...
Consider the region R between the x-axis and the curve y = x^3 /
3 , between x = 0 and x = 1.
(a) Calculate the surface area of the solid obtained by
revolving R about the x-axis.
(b) Write an integral for the the surface area of the solid
obtained by revolving R about the y-axis
Sketch the region enclosed by the given curves.
y = 8 cos
8x, y = 8 − 8 cos
8x, 0 ≤ x ≤
π/6
I already have the sketch however I need its Area
A) Find its area