Week 7 Test - Grade: 85%
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Questions Limits Points Due Date
20 Questions 180 Minutes 100 pts possible No due date.
Attempt 1 85% (85 of 100) Completed on 04/19/25 at 11:48PM
Score for this quiz: 85% ( 85 /100)
Submitted Apr 19 at 11:48pm
This attempt took about 1 hour.
Question 1 : 5 ptsSkip to question text.
Evaluate.∫−13(5−x) dxEvaluate.∫−13(5−x) dx
5
9
16
12
∫−13(5−x) dx=(5x−x22)∣∣∣3−1=(5⋅3−322)−(5⋅(−1)−(−1)22)=(15−92)−(−5−12)=(212)−(−112)=16∫−13(5−x)
dx=(5x−x22)−13=(5⋅3−322)−(5⋅(−1)−(−1)22)=(15−92)−(−5−12)=(212)−(−112)=16
5 /5
, Question 2 : 5 ptsSkip to question text.
Use the Fundamental Theorem of Calculus to find an expression for the derivative of the given function defined on the given interval, if it
exists.
F(x)=∫x13 dt, [1, 1000]F(x)=∫1x3 dt, [1, 1000]
F′(x)=2 on [1, 1000]F′(x)=2 on [1, 1000]
F′(x)=3 on [1, 1000]F′(x)=3 on [1, 1000]
F′(x)=0 on [1, 1000]F′(x)=0 on [1, 1000]
F′(x) is not defined over all of [1, 1000].F′(x) is not defined over all of [1, 1000].
None of these
With f(t)=3, which is continuouson [1, 1000], the integral isF(x)=∫x1f(t)dt. By the FundamentalTheorem of Calculus,
Part I, F′(x)=f(x)=3.With f(t)=3, which is continuouson [1, 1000], the integral isF(x)=∫1xf(t)dt. By the FundamentalTheor
em of Calculus, Part I, F′(x)=f(x)=3.
0 /5
Question 3 : 5 ptsSkip to question text.
Evaluate the indefinite integral∫⎛⎝⎜x2+2x+1x+1⎞⎠⎟ dx.Evaluate the indefinite integral∫(x2+2x+1x+1) dx.
x22+xx22+x
12(x2+2x+1x+1)212(x2+2x+1x+1)2
x22+x+Cx22+x+C
None of these
x2+2x+1x+1=(x+1)2x+1=x+1∫⎛⎝⎜x2+2x+1x+1⎞⎠⎟ dx=∫(x+1) dx
=x22+x+Cx2+2x+1x+1=(x+1)2x+1=x+1∫(x2+2x+1x+1) dx=∫(x+1) dx =x22+x+C
5 /5
Question 4 : 5 ptsSkip to question text.
Evaluate the indefinite integral∫ex+44 dx.Evaluate the indefinite integral∫ex+44 dx.
e2x+88+Ce2x+88+C
e2x4+Ce2x4+C
e2x+48+Ce2x+48+C
ex+44+Cex+44+C
ex+44=e44ex∫ex+44 dx=∫e44ex dx =e44∫ex dx =e4ex4+C =ex+44+Cex+44=e44ex∫ex+44 dx=∫e44ex dx =e44∫ex
dx =e4ex4+C =ex+44+C
5 /5
Question 5 : 5 ptsFind a function whose derivative is 1.
Find a function whose derivative is 1.
1
Instructions:
Click “Start” to begin the Test.
This Test may be printed by clicking the Print icon at the top of the Test window AFTER starting the Test.
We suggest you work out the answers on the printed Test, then submit your answers online.
THIS IS A TIMED TEST. YOU HAVE 3 HOURS TO COMPLETE THE TEST ONCE YOU CLICK "START." You can start and stop the Test if you
need to; however, the time will continue to elapse. You can also skip questions and go back to them as needed during the test. Use the 'skip'
button to skip a question and question navigation pull-down menu to jump back to any questions you skipped.
Once you have completed the Test online, click “Submit Answers.” Your answers will be scored and the answer key with step-by-step
solutions will become available.
Questions? Reach out to us at . We’re here and happy to help.
Questions Limits Points Due Date
20 Questions 180 Minutes 100 pts possible No due date.
Attempt 1 85% (85 of 100) Completed on 04/19/25 at 11:48PM
Score for this quiz: 85% ( 85 /100)
Submitted Apr 19 at 11:48pm
This attempt took about 1 hour.
Question 1 : 5 ptsSkip to question text.
Evaluate.∫−13(5−x) dxEvaluate.∫−13(5−x) dx
5
9
16
12
∫−13(5−x) dx=(5x−x22)∣∣∣3−1=(5⋅3−322)−(5⋅(−1)−(−1)22)=(15−92)−(−5−12)=(212)−(−112)=16∫−13(5−x)
dx=(5x−x22)−13=(5⋅3−322)−(5⋅(−1)−(−1)22)=(15−92)−(−5−12)=(212)−(−112)=16
5 /5
, Question 2 : 5 ptsSkip to question text.
Use the Fundamental Theorem of Calculus to find an expression for the derivative of the given function defined on the given interval, if it
exists.
F(x)=∫x13 dt, [1, 1000]F(x)=∫1x3 dt, [1, 1000]
F′(x)=2 on [1, 1000]F′(x)=2 on [1, 1000]
F′(x)=3 on [1, 1000]F′(x)=3 on [1, 1000]
F′(x)=0 on [1, 1000]F′(x)=0 on [1, 1000]
F′(x) is not defined over all of [1, 1000].F′(x) is not defined over all of [1, 1000].
None of these
With f(t)=3, which is continuouson [1, 1000], the integral isF(x)=∫x1f(t)dt. By the FundamentalTheorem of Calculus,
Part I, F′(x)=f(x)=3.With f(t)=3, which is continuouson [1, 1000], the integral isF(x)=∫1xf(t)dt. By the FundamentalTheor
em of Calculus, Part I, F′(x)=f(x)=3.
0 /5
Question 3 : 5 ptsSkip to question text.
Evaluate the indefinite integral∫⎛⎝⎜x2+2x+1x+1⎞⎠⎟ dx.Evaluate the indefinite integral∫(x2+2x+1x+1) dx.
x22+xx22+x
12(x2+2x+1x+1)212(x2+2x+1x+1)2
x22+x+Cx22+x+C
None of these
x2+2x+1x+1=(x+1)2x+1=x+1∫⎛⎝⎜x2+2x+1x+1⎞⎠⎟ dx=∫(x+1) dx
=x22+x+Cx2+2x+1x+1=(x+1)2x+1=x+1∫(x2+2x+1x+1) dx=∫(x+1) dx =x22+x+C
5 /5
Question 4 : 5 ptsSkip to question text.
Evaluate the indefinite integral∫ex+44 dx.Evaluate the indefinite integral∫ex+44 dx.
e2x+88+Ce2x+88+C
e2x4+Ce2x4+C
e2x+48+Ce2x+48+C
ex+44+Cex+44+C
ex+44=e44ex∫ex+44 dx=∫e44ex dx =e44∫ex dx =e4ex4+C =ex+44+Cex+44=e44ex∫ex+44 dx=∫e44ex dx =e44∫ex
dx =e4ex4+C =ex+44+C
5 /5
Question 5 : 5 ptsFind a function whose derivative is 1.
Find a function whose derivative is 1.
1
