A graph of ƒ is shown above. The numbers shown represent the geometric area of each region. Evaluate the following definite integrals.

Question

A graph of ƒ is shown above. The numbers shown represent the geometric area of each region. Evaluate the following definite integrals.

a)  =

b)  =

c)  =

d)  =

Answer 1

Remember that the integral represents area under the curve (or between the curve and the x-axis, thus area above the curve counts as negative area.

Also, areas add to each other so

₁∫ ³f(x) dx =₁ ∫²f(x) dx + ₂∫³f(x) dx

and -2_a∫^bf(x) is just -2 times the area for that region.

Let me know if this helps.