What is the net area between #f(x) = 3x^2-x+2# and the x-axis over #x in [1, 2 ]#?

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Answer 1 · 2016-04-24T17:36:37

#7.5# square units

First draw a rough graph of the function to visualize where the area is and to decide the limits of integration to find the area.

graph{3x^2-x+2 [-4.39, 9.66, -0.92, 6.107]}

Since #f(x)>=0 AAx in RR#, we may integrate directly over the entire given interval in order to find the area bounded, and it is given by

#A=int_1^2(3x^2-x+2)dx#

#=[x^3-1/2x^2+2x]_1^2#

#=(8-2+4)-(1-1/2+2)#

#=7.5#