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Application of definite integrals (FAQs)

Four mark questions

1. Find the area bounded by the curve y=x2-1, x-axis and the ordinates x=0 and x=2.

Suggested answer:

[pic]

Area =[pic] where [pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

2. Find the area bounded by y=sinx, x-axis between x=0 and [pic].

Suggested answer:

[pic]

By symmetry,

[pic]

[pic]

= [-0+1]

= 4 sq. units

3. Find the area of the region bounded by the line 2y=-x+8, x-axis and the ordinates x=2 and x=4.

Suggested answer:

[pic]

[pic]

In the given interval y is positive.

[pic]

[pic]

[pic]

= 5 sq. units

4. Find the area of the region between the curve y2=4x and x=3.

Suggested answer:

[pic]

y2 = 4x and x=3

A = Area OABC

= 2 Area OAB

[pic]

[pic]

[pic]

[pic]

[pic]

5. Find the area of region between the parabola y2=4ax and its latus rectum.

Suggested answer:

[pic]

y2=4ax and its L.R is x=a

A = Area OLSL|

= 2 Area OLS

[pic]

[pic]

[pic]

[pic]

[pic]

6. Find the area enclosed by the curve

y=x2-2x and x-axis.

Suggested answer:

[pic]

y=x2-2x …(i)

y+1=x2-2x+1

y+1=(x-1)2

This is a parabola of the form

(x-h)2=4a (y-k) whose vertex is [pic]

Parabola (1) meets x-axis when y=0,

[pic] 0=x2-2x [pic] x(x-2)=0

[pic] x=0,x=2

Required area is

[pic]

[pic]

7. Find the area enclosed between the parabolas y2=4ax and x2=4ay.

Suggested answer:

[pic]

Curves are [pic]

Points of intersection of the curves can be obtained by solving these equations.

[pic]

[pic] x4=64a3x

[pic] x(x3-43a3)=0...