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Mathematics
Mathematics
Problem
Let
f
f
f
be differentiable for
x
≥
0
x\ge 0
x
≥
0
with derivative
f
′
(
x
)
=
k
x
e
−
x
2
f'(x)=k x e^{-x^{2}}
f
′
(
x
)
=
k
x
e
−
x
2
, where
k
k
k
is a positive constant. Express the accumulated change in
f
f
f
from
x
=
0
x=0
x
=
0
to
x
=
a
x=a
x
=
a
(
a
>
0
a>0
a
>
0
) in terms of
a
a
a
and
k
k
k
.
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