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area between curves

0 votes
1) Find the area of the region bounded by the curves y= sqrt(x+2), y= 1/(x+1), x = 0,and x =2.

2) Find the area of the region bounded by the curves y=1-2x^2 and y = lxl.

3) Find the area of the region bounded by the curves x+y=0 and x= y^2+3y
asked May 5, 2015 in CALCULUS by anonymous

3 Answers

0 votes

(2)

Step 1 :

The curve equations are image and .

Graph the curves image and .

image

Observe the graph:

The points of intersection are image and image.

Step 2 :

The area between the curves is symmetrical about the y - axis.

Thus, area of the region is .

Observe the graph :

Upper curve is image.

Lower curve is .

Since we are only using the positive side of , consider image as image.

The boundaries are image and image.

image

image

Area of the region enclosed by the curves is 0.583 sq-units.

Solution:

Area of the region enclosed by the curves is 0.583 sq-units.

answered May 5, 2015 by yamin_math Mentor
0 votes

(1)

Step 1:

The curves are image, image.

Vertical lines are image and image.

Let image and image.

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.

Integral limits are image and image.

image

image

image

Apply power rule of integration: image.

image

image

image

answered May 5, 2015 by Sammi Mentor
edited May 5, 2015 by Sammi

Contd...

image

image

image

image

image

image

image

image

image

image

image

image sq-units.

Area of the region bounded by the curves is image sq-units.

Solution:

Area of the region bounded by the curves is image sq-units.

0 votes

(3)

Step 1 :

The curve equations are and .

Graph the curves  and .

Observe the graph:

The points of intersection are  and .

Rewrite the curve equations.

image.

.

Step 2 :

The area of the region is .

image

Area of the region enclosed by the curves is 10.667 sq-units.

Solution:

Area of the region enclosed by the curves is 10.667 sq-units.

answered May 5, 2015 by yamin_math Mentor
edited May 5, 2015 by yamin_math

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