AP Calculus AB Quiz
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INTEGRATION AND ACCUMULATION OF CHANGE
Question 1
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Suppose
U
(
x
)
=
∫
1
x
e
t
t
d
t
U(x)=\int_{1}^{x}\dfrac{e^{t}}{t}\,dt
U
(
x
)
=
∫
1
x
t
e
t
d
t
for
x
>
0
x>0
x
>
0
. What is
U
′
(
x
)
U'(x)
U
′
(
x
)
?
A
e
x
x
\dfrac{e^{x}}{x}
x
e
x
B
e
x
x
−
e
x
x
2
\dfrac{e^{x}x-e^{x}}{x^2}
x
2
e
x
x
−
e
x
C
∫
1
x
e
t
t
d
t
\int_{1}^{x}\dfrac{e^{t}}{t}\,dt
∫
1
x
t
e
t
d
t
D
e
t
t
\dfrac{e^{t}}{t}
t
e
t
E
[
∫
e
t
t
d
t
]
1
x
\left[\int \dfrac{e^{t}}{t}\,dt\right]_{1}^{x}
[
∫
t
e
t
d
t
]
1
x
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