Evaluate each integral by making an appropriate substitution
(a)
(c)
2. Find the area c The regionbounded above by the graph of g(x) and below by the
graph of f(x)= +2r-2.
3.
Let R be the closed regionbetween the graphs of y: 2x on the interval
[0. 1]. Find the volume of the solid obtained by revolving R about the a axis.
4.
Let R be the closed region between the graphs of y= 2x on the interval
[0. 1]. Find the volume of the solid obtained by revolving about the y- axis (Same
graph for Problem3)
5. Find the length of are on the graph of
from x=4
6. Find the area of the surface generated by revolving about the x-axis the curve
7. Fill in the values o -(x) and for = = 1,2,3 Provide detail b support
your answers
((x) f'(x) f-ยน(x) - (f-1)(x)
3
3
8 Calculate the derivative for
9. Use the definition an improper integral evaluate the following inregrals If an
integral converges evaluate value.
(a) 6-85ds
(b)
10. Using the indicated techniques to evaluate the following integrals Show work detail
tosuppon your solutions Solving using other methodso with no detail not acceptable
(a)
(Trigonometric substitution)
V1-452
(b)
(Trigonometric substitution)
(c)
(Inregration by Parts)
11 Complete the square the denominator make appropriate substitution and integrate.
5
12. Find the partial fraction decomposition for the rational function
and
-2)(u+3)
5
then evaluate the integral du
13. State whether the sequence converges diverges. Ifit converges, find its limit
(n
14. Using the Integral Test to test the following series for convergence Solving using
other methods or with no detail not acceptable
5
15. Determine whether the following series converge diverge. Indicate the test you use
1+sin k
(a)
k-1
4m-1
(b)
16. Determine whether the series convergesordiverges.
Ifit
converges, find sum
17. Determine whether the series converges conditionally converges
(-1)"
-551+3
absolutely. or diverges and givereasons for your conclusions
18. Find the interval of convergence for the power series Eve
e"-1
19. Use substitution method and known power series find power series for
x
Please express your answer in one sigma notation.

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