MathDB
Problems
Contests
National and Regional Contests
Japan Contests
Today's Calculation Of Integral
2010 Today's Calculation Of Integral
647
Today's calculation of Integral 647
Today's calculation of Integral 647
Source:
September 17, 2010
calculus
integration
trigonometry
logarithms
calculus computations
Problem Statement
Evaluate
∫
0
π
x
p
x
cos
q
x
d
x
,
∫
0
π
x
p
x
sin
q
x
d
x
(
p
>
0
,
p
≠
1
,
q
∈
N
+
)
\int_0^{\pi} xp^x\cos qx\ dx,\ \int_0^{\pi} xp^x\sin qx\ dx\ (p>0,\ p\neq 1,\ q\in{\mathbb{N^{+}}})
∫
0
π
x
p
x
cos
q
x
d
x
,
∫
0
π
x
p
x
sin
q
x
d
x
(
p
>
0
,
p
=
1
,
q
∈
N
+
)
Own
Back to Problems
View on AoPS