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Aus Online Mathematik Brückenkurs 2

The graph of the function y=2x+1 is a straight line which cuts the y -axis at y=1 and has gradient 2.

The integral's value is the area under the straight line and between x=0 and x=1.

We can divide up the region under the graph into a square and rectangle,

and then add up the area to obtain the total area.

The value of the integral is

102x+1dx=  (area of the square) + (area of the triangle) 11+2112=2