In this question, you are asked to investigate the following improper integral: (х-3) -13 dx 10.1 Firstly, one must split the integral as the sum of two integrals, i.e. 9 (x-3 )-1/3dx + lim (х-3) -13dx I= lim for what value of c? c = 10.2 Below, we will call the two integrals we split I into, I, and I. Now find an antiderivative of the integrand of I, (and I, and I), i.e. a function F(x), which when evaluated at the limits of Ig, will give the value of Ig. F(x) = 10.3 Now evaluate F(x) at each of the limits for I, and hence give the value of Ig. Note. By I, we mean the integral with an s limit, before the limit s c is taken. I, = 10.4 Now take the limit as s c, where c is your answer to the first part. If I, diverges as s c, enter u (for undefined), or if I, converges, enter the value to which I, converges.

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter8: Further Techniques And Applications Of Integration
Section8.2: Integration By Parts
Problem 32E
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In this question, you are asked to investigate the following improper integral:
9
I=
(х-3) -13dx
10.1
Firstly, one must split the integral as the sum of two integrals, i.e.
I= lim
(х-3) -13dx-
lim
(х-3) -13dx
t-c*
t
for what value of c?
10.2
Below, we will call the two integrals we split I into, I, and I.
Now find an antiderivative of the integrand of I, (and I, and I), i.e. a function F(x), which when evaluated at the limits of I, will give the value of Ig.
F(x) =
10.3
Now evaluate F(x) at each of the limits for I, and hence give the value of Ig.
Note. By Ig, we mean the integral with an s limit, before the limit s → c is taken.
I =
10.4
Now take the limit as s →c¯, where c is your answer to the first part.
If I, diverges as s →c, enter u (for undefined), or if Is converges, enter the value to which Iş converges.
lim, →e- Is =
Transcribed Image Text:In this question, you are asked to investigate the following improper integral: 9 I= (х-3) -13dx 10.1 Firstly, one must split the integral as the sum of two integrals, i.e. I= lim (х-3) -13dx- lim (х-3) -13dx t-c* t for what value of c? 10.2 Below, we will call the two integrals we split I into, I, and I. Now find an antiderivative of the integrand of I, (and I, and I), i.e. a function F(x), which when evaluated at the limits of I, will give the value of Ig. F(x) = 10.3 Now evaluate F(x) at each of the limits for I, and hence give the value of Ig. Note. By Ig, we mean the integral with an s limit, before the limit s → c is taken. I = 10.4 Now take the limit as s →c¯, where c is your answer to the first part. If I, diverges as s →c, enter u (for undefined), or if Is converges, enter the value to which Iş converges. lim, →e- Is =
10.5
Now evaluate F(x) at each of the limits for I, and hence give the value of I.
Note. By I,, we mean the integral with an t limit, before the limit t → c* is taken.
I =
10.6
Now take the limit as t → c", where c is your answer to the first part.
If I, diverges as t→ c", enter u (for undefined), or if I, converges, enter the value to which I, converges.
lim; e* I4 =
10.7
Finally, evaluate I.
If I is divergent enter u (for undefined), or if I is convergent enter the value to which I converges.
I=
Transcribed Image Text:10.5 Now evaluate F(x) at each of the limits for I, and hence give the value of I. Note. By I,, we mean the integral with an t limit, before the limit t → c* is taken. I = 10.6 Now take the limit as t → c", where c is your answer to the first part. If I, diverges as t→ c", enter u (for undefined), or if I, converges, enter the value to which I, converges. lim; e* I4 = 10.7 Finally, evaluate I. If I is divergent enter u (for undefined), or if I is convergent enter the value to which I converges. I=
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