School

Ball State UniversityDepartment

Mathematical SciencesCourse Code

MATH 165Professor

AllStudy Guide

FinalThis

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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) = e−xfrom 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

actual area. Justify your answer.

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

0√16 −x2dx by interpreting the

integral as area and using geometry.

6. If F(x) = R3

√x

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

−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

x2−x+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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