MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Today's Calculation Of Integral
2010 Today's Calculation Of Integral
664
664
Part of
2010 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 664
Source:
1/12/2011
For a positive integer
n
n
n
, let
I
n
=
∫
−
π
π
(
π
2
−
∣
x
∣
)
cos
n
x
d
x
I_n=\int_{-\pi}^{\pi} \left(\frac{\pi}{2}-|x|\right)\cos nx\ dx
I
n
=
∫
−
π
π
(
2
π
−
∣
x
∣
)
cos
n
x
d
x
.Find
I
1
+
I
2
+
I
3
+
I
4
I_1+I_2+I_3+I_4
I
1
+
I
2
+
I
3
+
I
4
.1992 University of Fukui entrance exam/Medicine
calculus
integration
trigonometry
calculus computations