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Final

# MATH 165 Ball State Final ReviewExam

Department
Mathematical Sciences
Course Code
MATH 165
Professor
All
Study Guide
Final

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Review Sheet - Final
1. Find the sum 5
X
i=1
i2.
2. In approximating the area under the graph
of f(x) = exfrom x=2 to x= 1 us-
ing nequally spaced rectangles with x
ibe-
ing the right endpoint, does your approx-
imation overestimate or underestimate the
3. Set up the sum to use the Midpoint Rule
with n= 4 to approximate R3
1x2dx.
4. Express the following as a single integral:
Z3
1
f(x)dx +Z7
5
f(x)dx
Z3
5
f(x)dx + 3 Z7
1
g(x)dx.
5. Evaluate R4
016 x2dx by interpreting the
integral as area and using geometry.
6. If F(x) = R3
x
01 + t4dt, what is F(x)?
7. If F(x) = Rx
02t3t2dt, what is the maxi-
mum value of Fon the interval [0,1]?
8. Find the area under the graph y=x2
2x+
3 from x= 0 to x= 3.
9. Find the area under the graph of y=2
1+x2
from x= 0 to x=3.
10. Compute Rsin x+1
x+1
x2dx.
11. Evaluate R4
1
x2x+1
xdx.
12. Evaluate Rln 6
ln 3 8exdx.
13. Evaluate R3
7x(x2+ 1)1/2dx.
14. Evaluate Rxcos(x2+ 1) dx.
15. Evaluate R3
7(cos x)esin xdx.
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