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Exam 142: Math Problem Solving - Spring 1999, Exams of Calculus

The University of Tennessee (UT)Calculus

Solutions to various math problems from exam 142 in spring 1999. The problems involve determining areas, volumes, and finding integrals of functions. The methods used include setting up integrals and solving using calculators.

Typology: Exams

Pre 2010

Uploaded on 08/31/2009

koofers-user-30n
koofers-user-30n 🇺🇸

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Math 142 Exam 2 Spring 1999 Name
No Work-No Credit SS#
1) Determine the area of the region bounded by x + y2 = 2, x + y = 2.
(sketch the region, set up the integral then solve.)
∫=−−−
1
0
2
6
1
)}2()2{( dyyy
2) Revolve the region bounded by y = x2, y = - x2, x = 1, x = 2 about the line x = -3 and
determine the volume of the solid generated. (First set up the integral, then you may
solve using the calculator)
(
)
∫≈+
2
1
209.135)2(32 dxxxπ
pf3

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Math 142 Exam 2 Spring 1999 Name

No Work-No Credit SS#

  1. Determine the area of the region bounded by x + y 2 = 2, x + y = 2. (sketch the region, set up the integral then solve.)

1 0

2

6

{( 2 y ) ( 2 y )} dy

  1. Revolve the region bounded by y = x

2 , y = - x

2 , x = 1, x = 2 about the line x = -3 and

determine the volume of the solid generated. (First set up the integral, then you may

solve using the calculator)

∫ (^ + ) ≈

2 2 2 π x 3 ( 2 x ) dx 135. 09

  1. Revolve the region determined by y = sin

4 x , x = 0, x = π, y = 0 , about the x-axis

and determine the volume of the solid generated. (Set up the integral, then solve using

the TI-86)

4 2 Ai = π (sin x ) , then Vi xdx

8

= π sin so ∫ ≈

π π 0

8 sin xdx 2. 699

  1. Determine the circumference of the ellipse given in parametric form:

x = 2 cos t y = sin t (^0) ≤ t ≤ 2 π

4 sin cos 9. 69

2 2 2

L = ∫ t + t dt ≈

π