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Today's Calculation Of Integral
2006 Today's Calculation Of Integral
115
115
Part of
2006 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 115
Source: Chiba University entrance exam 1977
7/7/2006
Find the value of
a
a
a
such that
∫
0
π
2
(
sin
x
+
a
cos
x
)
3
d
x
−
4
a
π
−
2
∫
0
π
2
x
cos
x
d
x
=
2.
\int_{0}^\frac{\pi}{2}(\sin x+a\cos x)^{3}\ dx-\frac{4a}{\pi-2}\int_{0}^{\frac{\pi}{2}}x\cos x dx=2.
∫
0
2
π
(
sin
x
+
a
cos
x
)
3
d
x
−
π
−
2
4
a
∫
0
2
π
x
cos
x
d
x
=
2.
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integration
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