area between curves

Question

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

Answer 1

(2)

Step 1 :

The curve equations are and .

Graph the curves and .

Observe the graph:

The points of intersection are  and .

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 .

Lower curve is .

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

The boundaries are and .

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.

Answer 2

(1)

Step 1:

The curves are , .

Vertical lines are and .

Let and .

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

.

Integral limits are and .

Apply power rule of integration: .

Comments

Contd...

sq-units.

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

Solution:

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

Answer 3

(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.

.

.

Step 2 :

The area of the region is .

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.