Calculate the area of the region bounded by the parabolas y² = 6x and x² =6y.

Find the area of the region common to the parabolas 4y² = 9x and 3 x² =16y.

Find the area of the region bounded by y = √x and y = x

Find the area bounded by the curve y = 4 – x² and the lined y = 0, y = 3.

Find the area of the region .

Using integration find the area of the region bounded by the triangle whose vertices are (2,1), (3,4) and (5,2).

Using integration, find the area of the region bounded by the triangle ABC whose vertices A, B, C are ( – 1,1), (0,5) and (3,2) respectively.

Using integration, find the area of the triangular region, the equations of whose sides are y = 2x + 1, y = 3x + 1 and x = 4.

Find the area of the region {(x, y) : y²≤8x, x² + y²≤ 9}

Find the area of the region common to the circle x² + y² = 16 and the parabola y² = 6x.

Find the area of the region between circles x² + y² = 4 and (x – 2)² + y² = 4.

Find the area of the region included between the parabola y² = x and the line x + y = 2.

Draw a rough sketch of the region {(x, y) : y² ≤ 3x, 3x² + 3y² ≤ 16} and find the area enclosed by the region using method of integration.

Draw a rough sketch of the region {(x,y) : y² ≤ 5x, 5x² + 5y² ≤ 36} and find the area enclosed by the region using the method of integration.

Draw a rough sketch and find the area of the region bounded by the two parabolas y² = 4x and x² = 4y by using methods of integration.

Find the area included between the parabolasy² = 4ax and x² = 4by.

Prove that the area in the first quadrant enclosed by the axis, the line x = √3y and the circle x² + y² = 4 is π/3.

Find the area of the region bounded by by y = √x and x = 2y + 3 in the first quadrant and x - axis.

Find the area common to the circle x² + y² = 16 a² and the parabola y² = 6ax.

OR

Find the area of the region {(x,y):y² ≤ 6ax} and {(x,y):x² + y² ≤ 16a²}.

Find the area, lying above x - axis and included between the circle circle x² + y² = 8x and the parabola y² = 4x.

Find the area enclosed by the parabolas y = 5x² and y = 2x² + 9.

Prove that the area common to the two parabolas y = 2x² and y = x² + 4 is 32/3 sq. Units.

Using integration, find the area of the region bounded by the triangle whose vertices are

(i) ( – 1, 2), (1, 5) and (3, 4)

(ii) ( – 2, 1), (0, 4) and (2, 3)

Find the area of the region bounded by y = √x and y = x.

Find the area of the region in the first quadrant enclosed by the x - axis, the line y = √3x and the circle x² + y² = 16.

Find the area of the region bounded by the parabola y² = 2x + 1 and the line x – y – 1 = 0.

Find the area of the region bounded by the curves y = x – 1 and (y – 1)² = 4 (x + 1).

Find the area enclosed by the curve y = – x² and the straight line x + y + 2 = 0

Find the area enclosed by the curve Y = 2 – x² and the straight line x + y = 0.

Using the method of integration, find the area of the region bounded by the following line 3x – y – 3 = 0, 2x + y – 12 = 0, x – 2y – 1 = 0.

Sketch the region bounded by the curves y = x² + 2, y = x, x = 0 and x = 1. Also, find the area of the region.

Find the area bounded by the curves x = y² and x = 3 – 2 y².

Using integration, find the area of the triangle ABC coordinates of whose vertices are A (4, 1), B (6, 6) and C (8, 4).

Using integration find the area of the region {(x,y)|x – 1| ≤ y ≤ √5 – x²}.

Find the area of the region bounded by y – |x – 1| and y = 1.

Find the area of the region bounded by y = x and circle x² + y² = 32 in the 1^st quadrant.

Find the area of the circle x² + y² = 16 which is exterior the parabola y² = 6x.

Find the area of the region enclosed by the parabola x² = y and the line y = x + 2.

Make a sketch of the region{(x,y): 0 ≤ y ≤ x² + 3; 0 ≤ y ≤ 2x + 3; 0 ≤ x ≤ 3} and find its area using integration.

Find the area of the region bounded by the curve y = √1 – x², line y = x and the positive x - axis.

Find the area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5.

Find the area of the region enclosed between the two curves x² + y² = 9 and (x – 3)² + y² = 9.

Find the area of the region {(x,y): x² + y² ≤ 4, x + y ≥ 2}

Using integration, find the area of the following region.

Using integration find the area of the region bounded by the curve , x² + y² – 4x = 0 and the x-axis.

Find the area enclosed by the curves y = |x – 1| and y = – |x – 1| + 1.

Find the area enclosed by the curves 3x² + 5y = 32 and y = |x – 2|.

Find the area enclosed by the parabolas y = 4x – x² and y = x² – x.

In what ratio does the x-axis divide the area of the region bounded by the parabolas y = 4x – x² and y = x² – x?

Find the area of the figure bounded by the curves y = |x – 1| and y = 3 – |x|.

If the area bounded by the parabola y² = 4ax and the line y = mx is a²/12 sq. Units, then using integration, find the value of m.

If the area enclosed by the parabolas y² = 16ax and x² = 16ay, a>0 is 1024/3 square units, find the value of a.