using integrals find the area of the region bounded by the line 2x-y+2=0, the x-axis and the ordinates x=-3 and x=0

Answer 1

To find the area under the graph of the function y=f(x)=2x+2 we need to know where f(x) changes from positive to negative. This happens at the point x=-1. So the total area under the graph from -3 to 0 it is equal to

-(integral of f(x) from -3 to -1) + (integral of f(x) from -1 to 0)= -(-4)+1=4+1=5.