Find the exact value of
c
>
0
\displaystyle {c}>{0}
c
>
0
such that the area of the region enclosed by the parabolas
y
=
x
2
−
c
2
\displaystyle {y}={x}^{{2}}-{c}^{{2}}
y
=
x
2
−
c
2
and
y
=
c
2
−
x
2
\displaystyle {y}={c}^{{2}}-{x}^{{2}}
y
=
c
2
−
x
2
is
40
\displaystyle {40}
40
.
c
=
\displaystyle {c}=
c
=
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