MATH 165 Ball State Final ReviewExam
SchoolBall State University
Course CodeMATH 165
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Review Sheet - Final
1. Find the sum 5
2. In approximating the area under the graph
of f(x) = e−xfrom x=−2 to x= 1 us-
ing nequally spaced rectangles with x∗
ing the right endpoint, does your approx-
imation overestimate or underestimate the
actual area. Justify your answer.
3. Set up the sum to use the Midpoint Rule
with n= 4 to approximate R3
4. Express the following as a single integral:
f(x)dx + 3 Z7
5. Evaluate R4
0√16 −x2dx by interpreting the
integral as area and using geometry.
6. If F(x) = R3
0√1 + t4dt, what is F′(x)?
7. If F(x) = Rx
02t−3t2dt, what is the maxi-
mum value of Fon the interval [0,1]?
8. Find the area under the graph y=x2
3 from x= 0 to x= 3.
9. Find the area under the graph of y=2
from x= 0 to x=√3.
10. Compute Rsin x+1
11. Evaluate R4
12. Evaluate Rln 6
ln 3 8exdx.
13. Evaluate R3
14. Evaluate Rxcos(x2+ 1) dx.
15. Evaluate R3
7−(cos x)esin xdx.
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