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Today's Calculation Of Integral
2012 Today's Calculation Of Integral
840
840
Part of
2012 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 840
Source: 2012 Ehime University entrance exam/Science
8/2/2012
Let
x
,
y
x,\ y
x
,
y
be real numbers. For a function
f
(
t
)
=
x
sin
t
+
y
cos
t
f(t)=x\sin t+y\cos t
f
(
t
)
=
x
sin
t
+
y
cos
t
, draw the domain of the points
(
x
,
y
)
(x,\ y)
(
x
,
y
)
for which the following inequality holds.
∣
∫
−
π
π
f
(
t
)
cos
t
d
t
∣
≤
∫
−
π
π
{
f
(
t
)
}
2
d
t
.
\left|\int_{-\pi}^{\pi} f(t)\cos t\ dt\right|\leq \int_{-\pi}^{\pi} \{f(t)\}^2dt.
∫
−
π
π
f
(
t
)
cos
t
d
t
≤
∫
−
π
π
{
f
(
t
)
}
2
d
t
.
calculus
integration
function
trigonometry
algebra
domain
inequalities