MATH 172 University of New Haven Sections 6 Calculus Practice Problems I uploaded the questions in the file the name of the textbook is Calculus by Rogaws

MATH 172 University of New Haven Sections 6 Calculus Practice Problems I uploaded the questions in the file the name of the textbook is Calculus by Rogawski, 3rd edition.let me know if you any questions 🙂 Math 172 Sections 6.5-7.1 Practice Problems
Name:
Due: Wednesday, 27 May, 9pm (MDT)
30 total points, point values in boxes .
If possible, print this and submit it to gradescope. If not, please clearly write the problems and your
solutions on your own paper.
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1. A cone of radius 6m and height 3m has volume 36π m3 . A cone of radius 3m and height 12 m has the
same volume. Both cones are oriented so that the point is up. The cone of radius 6 m is built out of
chocolate of density 1325 kg/m3 . The cone of radius 3 m is built out of marshmallow of density 500
kg/m3 . Determine which takes more work to build by finding the work to build each.
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2. After a long climb to the top of a beanstalk, Jack sees a giant drinking a murky red cocktail. The
interior of the glass is in the shape of a frustum with lower radius 1 m and upper radius 2 m. The
height of the interior of the glass is 4 m. The Blood of an Englishman1 cocktail she is drinking is has
a density of ρ. The giant is sipping her cocktail using a straw that extends 2 m past the top of the
glass. When Jack arrived the giant had already consumed the ‘top half’ (as measured by height, not
volume). How much work does the giant do by slurping the ‘bottom half’ up through the straw?
Express your solution as a definite integral; do not evaluate the integral. Please start by clearly
identifying the coordinate system that you will be using.
2m
2m
4m
1m
1
No Englishmen were harmed in the writing of this question. No blood of any kind was used for her cocktail; the giant is
a very pleasant vegan.
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3. Evaluate the following integrals.
Z
(a)
(1 − 3x)e2x dx
Z
4
(b)
ln (2x)
dx
x3
Z
4
4
(c)
arcsin (2x) dx
4. Use integration by parts to derive the reduction formula
Z
Z
n−1
1
n−1
n
x sin x +
cosn−2 x dx.
cos x dx = cos
n
n

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