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Today's Calculation Of Integral
2010 Today's Calculation Of Integral
669
669
Part of
2010 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 669
Source: 1978 Mie University entrance exam
7/3/2011
Find the differentiable function defined in
x
>
0
x>0
x
>
0
such that
∫
1
f
(
x
)
f
−
1
(
t
)
d
t
=
1
3
(
x
3
2
−
8
)
.
{\int_1^{f(x)} f^{-1}(t)dt=\frac 13(x^{\frac {3}{2}}-8}).
∫
1
f
(
x
)
f
−
1
(
t
)
d
t
=
3
1
(
x
2
3
−
8
)
.
calculus
integration
function
calculus computations