Find the area of the region bounded by y² = 9x, x = 2, x = 4 and the x - axis in the first quadrant.

3

(a)

Find the area of the region in the first quadrant enclosed by x - axis and \(x=\sqrt { 3 } y\) by the circle \({ x }^{ 2 }+{ y }^{ 2 }=4\).

3

(a)

The area between x = y² and x = 4 is divided into two equal parts by the line x = a, find the value of a.

3

(a)

Find the area bounded by the curve x² = 4y and the line x = 4y - 2.

3

(a)

Choose the correct answer:
Area lying between the curves y² = 4x and y = 2x is :
(A) \(\frac { 2 }{ 3 } \)
(B) \(\frac { 1 }{ 3 } \)
(C) \(\frac { 1 }{ 4 } \)
(D) \(\frac { 3 }{ 4 } \)

3

(a)

Choose the correct answer:
The area bounded by the curve \(y=x\left| x \right| \), x - axis and the ordinates x = -1 and x = 1 given by :
(A) 0
(B) \(\frac { 1 }{ 3 } \)
(C) \(\frac { 2 }{ 3 } \)
(D) \(\frac { 4 }{ 3 } \)

3

(a)

Find the area of the region bounded by the parabola y² = 2x and the straight line x - y = 4. 

3

(a)

Find the area of the region bounded by:
y² = 4x, x = 1, x = 4 and x - axis in the first quadrant. 

3

(a)

Using the method of integration, find the area of the region bounded by the lines:
3x - 2y + 1 = 0, 2x + 3y - 21 = 0 and x - 5y + 9 = 0

3

(a)

Find the area of the region given by:
\(\left\{ \left( x,y \right) :{ x }^{ 2 }\le y\le \left| x \right| \right\} \)

3

(a)

Find the area of smaller region bounded by the ellipse  \(\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } } =1\) and the straight line \(\frac { x }{ a } +\frac { y }{ b } =1\)  

4

(a)

Sketch the rough graph of the two parabolas 4y² = 9x and 3x² = 16y and find the area bounded by the two curves. 

4

(a)

using integration, find the area of the region bounded by the curves y = x² and y = x.

6

(a)

Using integration find the area of the region given by {(x,y) : (x²\(\le \)y\(\le \) |x|)}.

6

(a)