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Take Home Exam 1 - Calculus II - Fall 2007 | MATH 132, Exams of Calculus

Christian Brothers University (CBU)Calculus
Prof. Andrew M. Diener

Material Type: Exam; Professor: Diener; Class: Calculus II; Subject: Mathematics; University: Christian Brothers University; Term: Summer 2007;

Typology: Exams

Pre 2010

Uploaded on 08/18/2009

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koofers-user-maj 🇺🇸

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EXAM 1
Math 132
July 20, 2007
Name
1. Given that the velocity function is known to be v(t) = 40 −sin (t) with s(0) = 2, what is the
position function s(t). (7 pts)
2. Find the derivative d
dx Zx2
0.5
cos (t2+ 5) dt. (5 pts)
3. Find the area region contained in the curves y=x,y= 4 −x2and y= 0 (8 pts)
pf3
pf4
pf5

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Download Take Home Exam 1 - Calculus II - Fall 2007 | MATH 132 and more Exams Calculus in PDF only on Docsity!

EXAM 1

Math 132 July 20, 2007

Name

  1. Given that the velocity function is known to be v(t) = 40 − sin (t) with s(0) = 2, what is the position function s(t). (7 pts)
  2. Find the derivative

d dx

∫ (^) x 2

  1. 5

cos (t^2 + 5) dt. (5 pts)

  1. Find the area region contained in the curves y = x, y = 4 − x^2 and y = 0 (8 pts)
  1. Find each of the following integrals. No credit will be given for a correct answer which has no supporting arguments. (No, the statement “I used the calculator” is NOT a supporting argument.) (8 pts each)

(a)

x √ 4 − x^2

dx.

(b)

x^2 cos (3x) dx.

(c)

∫ π 4

0

sin (x) cos^4 x dx.

(d)

x

ln (x)

dx.

  1. Use the Trapezoid Rule with n = 27 to estimate the numerical value of

1

x dx. (6 pts)

  1. Find the volume created by rotating the region bounded by y = x^2 − 2 and y = x around the line x = 3. (6 pts)
  1. Write the integral needed to find the volume of the solid created by rotating the region bounded by y =

x, y = 2 and x = 0 about the line x = 4. (6 pts)

  1. Find the length of the curve y = ln (x) for 1 ≤ x ≤ 4. (6 pts)