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Finite Sum of Exponential Integrals and the Harmonic Number
Daily Problem
1 i's
Evaluate the integral
∫
0
∞
e
−
k
x
d
x
,
k
>
0
,
and compute
∑
k
=
1
10
∫
0
∞
e
−
k
x
d
x
.
\text{Evaluate the integral} \int_{0}^{\infty} e^{-kx}\,dx, \quad k>0, \\ \text{and compute} \sum_{k=1}^{10} \int_{0}^{\infty} e^{-kx}\,dx.
Evaluate the integral
∫
0
∞
e
−
k
x
d
x
,
k
>
0
,
and compute
k
=
1
∑
10
∫
0
∞
e
−
k
x
d
x
.
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