Question

4. Find the area of the region bounded by the curve y = 4 − x 2 and the line y = x + 2.

Answer #1

Find the area of the region bounded by the y-axis, the curve y =
ln(x+ 1),
and the tangent line to y = ln(x + 1) at x = 3.

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.

Find the area of the region in the ?? x y -plane bounded above
by the graph of the function ?(?)=9 , below by the ? -axis, on the
left by the line ?=8 , and on the right by the line ?=19 . The area
is

Consider the region bounded by y=sqrt(x) and y=x^3
a) Find the area of this region
b) Find the volume of the solid generated by rotating this
region about the x-axis using washer
c) Find the volume of the solid generated by rotating this
region about the horizontal line y=3 using shells

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...

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...

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

Find the area of the "triangular" region in the first quadrant that
is bounded above by the curve y=e^3x, below by the curve y=e^2x,
and on the right by the line x=ln2

Find the area of the region bounded by the graphs:
y=x^2-4
y=x^4-4x^2
I set the equations equal to one another then solved for zero,
but I am stuck after getting x^4-5x^2+4

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

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