Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>EXERCISE>Q 1

HARD

12th ICSE

IMPORTANT

Earn 100

Find the area of the region bounded by the curve $x y - 3 x - 2 y - 10 = 0$ , the $x - a x i s$ and the lines $x = 3, x = 4$ .

Important Questions on Applications of Integrals

HARD

12th ICSE

IMPORTANT

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

The area included between the x-axis and the curve

a^{2} y = x^{2} (x + a)

is

\frac{a^{2}}{k}

sq.units, then find the value of

3 {[\frac{x^{0 + 1}}{0 + 1}]}_{3}^{4} + 16 {[\log (x - 2)]}_{3}^{4} = 3 [4 - 3] + 16 [\log (2) - 0] = 3 + 16 \log (2)

.

HARD

12th ICSE

IMPORTANT

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

The area bounded by the $x - a x i s$ , part of the curve $y = 1 + \frac{8}{x^{2}}$ and the ordinates at $x = 2$ and $x = 4$ is $m$ . If the ordinate at $x = a$ divides the area into two equal parts, if $a = 2 \sqrt{k}$ .

Find the value of $m + k$

HARD

12th ICSE

IMPORTANT

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

Find the area bounded by the curves

y^{2} = 4 a (x + a)

and

y^{2} = 4 b (b - x)

.

HARD

12th ICSE

IMPORTANT

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

If the area enclosed by the curve

y = x^{3} - 6 x^{2} + 8 x

,

0 \leq x \leq 4

and the

x - a x i s

is

k

sq. units, then the value of

k

is

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 1

Find the area under the given curves and the given lines :
(i)

y = x^{2}, x = 1, x = 2

and

x - a x i s .

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 3 - Applications of Integrals>CHAPTER TEST>Q 1

Find the area under the given curves and the given lines :

(ii) $y = x^{4}, x = 1, x = 5$ and $x - a x i s .$

MEDIUM

12th ICSE

IMPORTANT

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

Find the area of the region lying in the first quadrant and bounded by

y = 4 x^{2}, x = 0, y = 1

and

y = 4 .

MEDIUM

12th ICSE

IMPORTANT

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

Find the area enclosed between the curve

y = 2 x - x^{2}

and the

x - a x i s

.