Verifying a Property Use a graph to explain why
if f is integrable on [a, b] and k is a constant.
To prove: The definite integrals .
Given: The property to be verified is,
Where is integrable on and is a constant.
Formula used: We know that area bounded by the graph of and -axis on interval is represented by,
Proof: Take a function which is integrable on
First we will draw the graph of for that substitute in .
Any line can be drawn using two points and the points are plot the points on the coordinate axes and shade the region to obtain,
This figure is a trapezoid of altitude and the parallel bases of and .
Using, to get,
Now, draw the graph of for that substitute in
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