MATH225 Calculus I Week 7 Test - Grade: 85% | Working Shown.

MATH225 Calculus I 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 pts 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 pts
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 pts
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 pts
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