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Today's Calculation Of Integral
2012 Today's Calculation Of Integral
859
859
Part of
2012 Today's Calculation Of Integral
Problems
(1)
Today's calculation of Integral 859
Source:
12/24/2012
In the
x
x
x
-
y
y
y
plane, for
t
>
0
t>0
t
>
0
, denote by
S
(
t
)
S(t)
S
(
t
)
the area of the part enclosed by the curve
y
=
e
t
2
x
y=e^{t^2x}
y
=
e
t
2
x
, the
x
x
x
-axis,
y
y
y
-axis and the line
x
=
1
t
.
x=\frac{1}{t}.
x
=
t
1
.
Show that
S
(
t
)
>
4
3
.
S(t)>\frac 43.
S
(
t
)
>
3
4
.
If necessary, you may use
e
3
>
20.
e^3>20.
e
3
>
20.
calculus
integration
geometry
derivative
calculus computations