application-integrals-help??

Question

Answer 1

(5)

Step 1:

The curve equations are and .

Find the area bounded by the curves  between and .

Area of the region bounded by the curves and between and is

Observe the graph :

The upper curve is .

The lower curve is .

Area bounded by the curves is 2 sq-units.

Solution :

Area bounded by the curves is 2 sq-units.

Answer 2

(6)

Step 1 :

The curves are , and about x - axis.

Consider .

Rewrite the equation.

.

Washer Method:

The volume of the solid S is , where  is the cross sectional area of the solid S.

Graph:

Graph the curves and .

Observe the graph.

Intersection points are x = 0 and x = 1.

Outer radius will be distance from the line to : .

Inner radius wlii be distance from the line to : .

Integral limits are x = 0 and x = 1.

Step 2 :

The volume of the solid is

Volume of the solid is cubic units.

Solution :

Volume of the solid is cubic units.