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GWU Calculus Worksheet

GWU Calculus Worksheet

GWU Calculus Worksheet

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Math 1231 Fall 2022
Single-Variable Calculus I Section 13
Mastery Quiz 11
Due Thursday, December 8
This weekàmastery quiz has two topics. Everyone should submit both.
Don worry if you make a minor error, but try to demonstrate your mastery of the
underlying material. Feel free to consult your notes, but please don discuss the actual quiz
questions with other students in the course.
Remember that you are trying to demonstrate that you understand the concepts involved.
For all these problems, justify your answers and explain how you reached them. Do not just
write es/r ¯/r give a single number.
Please turn this quiz in class on Thursday. You may print this document out and write
on it, or you may submit your work on separate paper; in either case make sure your name
and recitation section are clearly on it. If you absolutely cannot turn it in in person, you
can submit it electronically but this should be a last resort.
Topics on This Quiz

ajor Topic 5: Integration

ajor Topic 6: Applications of the Integral
Name:
Recitation Section:
1
Name:
Recitation Section:
M5: Integration
Z
(a) Compute
cos(5x + 3) dx.
Z 2
(b) By explicitly changing the bounds of integration, compute
?
x5 x3 + 8 dx.
1
Z 2
(c) Compute
0
?
x2
dx.
5×3 + 9
M6: Applications of Integrals
(a) Sketch the region bounded by the curves y = (x ? 1)2 and y = x + 1. Find the area of
the region.
(b) A spring with natural length of 30 cm takes 10 N of force to stretch to 40 cm. How
much work does it take to stretch it from 40 cm to 50 cm?
2

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