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Sketch the region bounded by the graphs of the algebraic functions and find the area of the region.

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Sketch the region bounded by the graphs of the algebraic functions and find the area of the region.

asked Feb 16, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The functions are and .

The vertical lines are and .

Graph:

Graph the functions are and .

Shade the region bounded by the curves between image and .

image

Note: The region shaded in blue color is the required area of region.

Step 2:

Definite integral as area of the region:

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

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

image.

Observe the graph:

Upper curve is image.

Lower Curve is image.

The vertical lines are image and .

Area of the region is

image

Area of the region is 2.166 sq-units.

Solution:

Graph the region of graph of  and between image and is

image

Area of the region is 2.166 sq-units.

answered Feb 18, 2015 by Lucy Mentor

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