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Today's Calculation Of Integral
2005 Today's Calculation Of Integral
83
Today's calculation of Integral 83
Today's calculation of Integral 83
Source: 2004 Kochi Women University Entarance Exam
September 10, 2005
calculus
integration
trigonometry
calculus computations
Problem Statement
Evaluate
∑
n
=
1
∞
∫
2
n
π
2
(
n
+
1
)
π
x
sin
x
+
cos
x
x
2
d
x
(
n
=
1
,
2
,
⋯
)
\sum_{n=1}^{\infty} \int_{2n\pi}^{2(n+1)\pi} \frac{x\sin x+\cos x}{x^2}\ dx\ (n=1,2,\cdots)
n
=
1
∑
∞
∫
2
nπ
2
(
n
+
1
)
π
x
2
x
sin
x
+
cos
x
d
x
(
n
=
1
,
2
,
⋯
)
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