You are given the four points in the plane A=(−5,−8), B=(0,1), C=(5,−3), and D=(7,8). The graph of the function f(x) consists of the three line segments AB, BC and CD. Find the integral ∫7−5f(x)dx by interpreting the integral in terms of sums and/or differences of areas of elementary figures.

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Step 1Please see the below picture for detailed solution. Step 2A=(-5,-8),B=(0,1),C=(5,-3),D=(7,8)equation of line AB is (x-0)/(0+5)=(y-1)/(-1+8)=>9x-5y+5=0:.5f(x)=5y=9x+5A_(1)=int_(-5)^(0)7-5f(x)dx=int_(-5)^(0)(2-9x)dx=[2x-(9)/(2)x^(2)]_(-5)^(0)=10+(225)/(2)equation of l ... See the full answer