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Today's Calculation Of Integral
2005 Today's Calculation Of Integral
88
Today's calculation of integral 88
Today's calculation of integral 88
Source: 1988 Meiji University entrance exam
November 16, 2005
calculus
integration
function
calculus computations
Problem Statement
A function
f
(
x
)
f(x)
f
(
x
)
satisfies
{
f
(
x
)
=
−
f
′
′
(
x
)
−
(
4
x
−
2
)
f
′
(
x
)
f
(
0
)
=
a
,
f
(
1
)
=
b
\begin{cases} f(x)=-f''(x)-(4x-2)f'(x)\\ f(0)=a,\ f(1)=b \end{cases}
{
f
(
x
)
=
−
f
′′
(
x
)
−
(
4
x
−
2
)
f
′
(
x
)
f
(
0
)
=
a
,
f
(
1
)
=
b
Evaluate
∫
0
1
f
(
x
)
(
x
2
−
x
)
d
x
.
\int_0^1 f(x)(x^2-x)\ dx.
∫
0
1
f
(
x
)
(
x
2
−
x
)
d
x
.
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