Sketch the graph of the function and shade the region whose area is represented by the integral.

Question

The integrand of the definite integral is a difference of two functions. Sketch the graph of the function and shade the region whose area is represented by the integral.

Answer 1

Step 1:

The area of the region is represented by the integral as .

Definite integral as area of the region:

If and are continuous and non-negative on the closed interval ,

then the area of the region bounded by the graphs of and and the vertical lines and is given by

.

Compare the integral with the general form of area of the region then

and .

Vertical lines are and .

Graph:

Graph the functions and .

Shade the region bounded by the curves between and .

Solution:

Graph of the area of the region represented by the integral is