Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 3

MEDIUM

12th ICSE

IMPORTANT

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Find the area enclosed between the curve $y = 2 x - x^{2}$ and the $x - a x i s$ .

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Important Questions on Applications of Integrals

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 4

Find the area of the region bounded by the parabola

y^{2} = 16 x

and its latus-rectum.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 5

Find the smaller area cut from the circle

x^{2} + y^{2} = 25

by the line

x = 3

.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 6

If the area of the region bounded by the triangle whose vertices are

(- 1, 0), (1, 3)

and

(3, 2)

is

k

sq. units, then the value of

k

is

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 7

If the area bounded by the parabola

y^{2} = 4 x

and

y = 2 x - 4

is

k

sq. units, then the value of

k

is

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 8

Find the area bounded by the curve

y^{2} = 4 a^{2} (x - 3)

and the lines

x = 3, y = 4 a

.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 9

Draw a rough sketch and find the area of the region bounded by the two parabolas

y^{2} = 8 x

and

x^{2} = 8 y

by using method of integration.

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 10

Using integration, find the area of the region

= \{(x, y) : x^{2} + y^{2} \leq 16, x^{2} \leq 6 y\} .

HARD

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 11

Find the area common to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} = 4 x$ .