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Use a graphing utility to graph the region bounded by the graphs of the equations

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(a) Use a graphing utility to graph the region bounded by the graphs of the equations, (b) find the area of the region, and (c) Use the integration capabilities of the graphing utility to verify your results.

asked Feb 16, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(a)

Step 1 :

The graphs of the equations are .

Sketch the region bounded by the graphs :

Graph the functions image and image.

Shade the region bounded by the curves between image and image.

image

Observe the graph for intersection points are image and image.

Solution:

Regions bounded by the graphs of equations is

 image

answered Feb 19, 2015 by yamin_math Mentor
0 votes

(b)

Step 1 :

The graphs of the equations are .

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

.

The area of the region bounded by the curves contains 3 sub regions as shown below.

Region R1 :

Upper curve : .

Lower curve : .

Region R2 :

Upper curve : .

Lower curve : .

Region R3 :

Upper curve : .

Lower curve : .

answered Feb 19, 2015 by yamin_math Mentor

Contd....

Step 2 :

 Area bounded by the curves :

image

 The area bounded by the region is imagesquare units.

Solution:

The area bounded by the region is imagesquare units.

0 votes

(c)

Step 1 :

The graphs of the equations are .

Verify the area region graphically :

Graphically the area bounded by region is 7.999 square units.

Solution:

The area bounded by the region is imagesquare units.

answered Feb 19, 2015 by yamin_math Mentor

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