Question

Each of the regions A, B, and C bounded by the graph of f and the x-axis has area 3. Find the value of

Answer 1

Answer:

  9

Step-by-step explanation:

You want the value of the given integral, when areas A, B, C are all 3.

Integral

The integral can be decomposed to the sum ...

  $\displaystyle\int_{-4}^2{[f(x)+2x+4]}\,dx=\int_{-4}^2{f(x)}\,dx+\int_{-4}^2{(2x+4)}\,dx\\\\\\=-3+3-3+[x^2+4x]_{-4}^2=-3+(2^2-(-4)^2)+4(2-(-4))\\\\\\=-3+(4-16)+4(2+4)=-3-12+24 =\boxed{9}$

The value of the integral is 9.