Question

Find the area under each of the given curves

a) ? = √?, ? = 0 ?? ? = 4 b) ? = (2? − 3)4, ? = 1 ?? ? = 4

Answer #1

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...

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.

Find the slope and the equations of the tangent lines to the
given curves at each of the given points.
1. ?=2cos? ?=3sin?
a. ?=?/4
b. ?=?/2

Find the area between the two curves ?(?) = ? − 5 and ?(?) = 3?
2 + 3? + 4 over the interval [−1, 2] (include a sketch of the
region):

Find the volume of the solid generated by revolving
the area bounded by the given
curves/lines about the indicated axis using both vertical and
horizontal elements if applicable.
y=x² ,x=1, y=0
a. about the axis
b. about x=1
c. about the y-axis

Sketch the region enclosed by the given curves and find its
area:
a)y=x^2-4
b)y=x+2 1<=x<=4

Find the area of the region between the curves ? = ? 2 + 5? + 4
and ? = 1 − ? 2 .

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

Given the following pairs of z-values, find the area
under the normal curve between each pair of z-values.
Refer to the table in Appendix B.1. (Round the final
answers to 4 decimal places.)
a. z = -0.3 and z = 2
b. z = -2.25 and z = -0.6
c. z = 1.45 and z = 2.71
d. z = -2.52 and z = 1.61

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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