MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Today's Calculation Of Integral
2005 Today's Calculation Of Integral
83
83
Part of
2005 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 83
Source: 2004 Kochi Women University Entarance Exam
9/10/2005
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
,
⋯
)
calculus
integration
trigonometry
calculus computations