Isaac H.

asked • 12/06/22

Evaluate the following integrals by interpreting them in terms of areas:

Consider the graph of the function f(x):

Evaluate the following integrals by interpreting them in terms of areas:


(a) \displaystyle \int_{0}^{\,2} {f(x)}\,dx =

(b) \displaystyle \int_{0}^{\,5} {f(x)}\,dx =

(c) \displaystyle \int_{5}^{\,7} {f(x)}\,dx =

(d) \displaystyle \int_{0}^{\,9} {f(x)}\,dx =


Mark M.

All of the areas can be calculated either by counting squares or by using formulas form Geometry. Attempt some, then ask for help.
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12/07/22

1 Expert Answer

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William W. answered • 12/07/22

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If you are trying to find the integral from 0 to 2 then you would find the area of the trapezoid shaded in blue below (or rectangle plus triangle):


Do the same on the others using the limits of integration that are noted.


Areas above the x-axis are positive. Areas below the x-axis are negative.

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