solving using integrals

Question

if I have a graph of f(x) and I want to find (on the top of the integral sign is 5, and on the bottom is -2)  ∫f(x)dx

 

what would ∫f(x)dx equal?... (if the graph has points at (-5,2) (-2,0) (0,2) (1,3) (3,3) (4,0) (5,-3) )

 

a.) 10.5

b.) 15.5

c.) 14

d.) 8.5

Answer 1

Since we don't know the formula for f(x), but know the points, the best way is to plot each of these points on a coordinate system.  Then you connect the points to obtain a definite curve.  Then, drawn small trapezoids and rectangles between x=-2 and x=5.  Find the area of each trapezoid and rectangle under this curve and combine them.

 

Remember that integration is the area under the curve.  Well, this is the exact process that we are doing.

 

 

Hope this helps you out!

 

:)