MathDB

Today's calculation of Integral 859

Source:

December 24, 2012

calculusintegrationgeometryderivativecalculus computations

Problem Statement

In the

x

y

plane, for

t>0

, denote by

S(t)

the area of the part enclosed by the curve

y=e^{t^2x}

, the

x

-axis,

y

-axis and the line

x=\frac{1}{t}.

Show that

S(t)>\frac 43.

If necessary, you may use

e^3>20.