On the interval

MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration

Problem

On the interval

[-\sqrt{6},\,\sqrt{6}]

, the curves

f(x)=x^{4}-6x^{2}+8

and

g(x)=2x^{2}-4

enclose several subregions. Compute the total area of all these enclosed regions. (a)

\displaystyle \frac{224}{15}\sqrt{2}-\frac{32}{5}\sqrt{6}

(b)

\displaystyle \frac{448}{15}\sqrt{2}+\frac{32}{5}\sqrt{6}

(c)

\displaystyle \frac{448}{15}\sqrt{2}-\frac{32}{5}\sqrt{6}

(d)

\displaystyle \frac{256}{15}\sqrt{2}-\frac{16}{5}\sqrt{6}