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The fall 2011 exam for math 101, including problems related to indefinite and definite integrals, sketching regions, setting up integrals for volumes, and solving an initial value problem. Students are required to show their work for full credit.
Typology: Exams
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Please write your final answer in the space provided. For full credit you must show your work. Good Luck!
(a) (5 points)
x dx (1a)
(b) (8 points)
∫ cos x sin^4 x
dx (1b)
3 x^3 √ 13 + x^4
dx
(2)
∫ (^3)
− 2
f (x) dx.
The total amount of water that flows out of the tank is given by I =
∫ (^10)
0
f (t) dt. Estimate I using M 5. (4)
(a) (8 points) Set up the integral you would use to find the volume of the solid generated by revolving R around the x-axis.
(7a)
(b) (8 points) Set up the integral you would use to find the volume of the solid generated by revolving R around the line x = 3.
(7b)
dy dt = y^2 t, y(1) = 2. Use Euler’s Method with 3 steps to estimate y(1.75). Do this by hand (writing out all steps and using a calculator only to perform basic operations). Round to 4 digits after the decimal point.
