Question

1) Find the area of the region bounded by the curves y = 2x^2 − 8x + 12 and y = −2x + 12

a) Find the volume when the area in question 1 is revolved around the x-axis.

b)Find the volume when the area in question 1 revolved around the y-axis.

Answer #1

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1. Find the area of the region between the curves y = x - 1 and
y2 = 2x + 6 .
2. Find the volume of the solid of revolution formed by rotating
the region about the y-axis bounded by y2 = x and x =
2y.

1- Find the area enclosed by the given curves.
Find the area of the region in the first quadrant bounded on the
left by the y-axis, below by the line above left
by y = x + 4, and above right by y = - x 2 + 10.
2- Find the area enclosed by the given curves.
Find the area of the "triangular" region in the first quadrant that
is bounded above by the curve , below by the curve y...

Find the area of the region bounded by the curves y=3x2 and
y=−8x+3. please show work. thanks

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.

1.Find the area of the region between the curves y= x(1-x) and y
=2 from x=0 and x=1.
2.Find the area of the region enclosed by the curves
y=x2 - 6 and y=3 between their
interaction.
3.Find the area of the region bounded by the curves
y=x3 and y=x2 between their interaction.
4. Find the area of the region bounded by y= 3/x2 ,
y= 3/8x, and y=3x, for x greater than or equals≥0.

A. For the region bounded by y = 4 − x2 and the x-axis, find
the volume of solid of revolution when the area is revolved
about:
(I) the x-axis,
(ii) the y-axis,
(iii) the line y = 4,
(iv) the line 3x + 2y − 10 = 0.
Use Second Theorem of Pappus.
B. Locate the centroid of the area of the region bounded by y
= 4 − x2 and the x-axis.

1- Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
?= 64x− 8x^2, y=0;
about the y-axis
2- Find the volume of the solid obtained by rotating the region
bounded by the given curves about the specified axis.
y= 5+ 1/x^2, y= 5, x=2, x=9;
about the x-axis.

Find the surface area of the solid generated when the
region bounded by x=ln(2y+1),0≤y≤1 is revolved about the Y-
axis.

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

5. Find the area bounded by the curves: two x = 2y - y^2 ; x =
0.
6. Find the surface area of the solid of revolution generated
by rotating the region along the x-axis. bounded by the curves: ? =
2?; y = 0 since x = 0 until x = 1

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