Find the area under the given curves and given lines:

y = x², x = 1, x = 2 and x-axis

Find the area under the given curves and given lines:

y = x₄, x = 1, x = 5 and x-axis

Find the area between the curves y = x and y = x².

Find the area of the region lying in the first quadrant and bounded by y = 4x², x = 0, y = 1 and y = 4.

Sketch the graph of y = |x+3| and evaluate

Find the area bounded by the curve y = sin x between x = 0 and x = 2π.

Find the area enclosed between the parabola y² = 4ax and the line y = mx.

Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x + 12.

Find the area of the smaller region bounded by the ellipse and the line

Find the area of the smaller region bounded by the ellipse line

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

Using the method of integration find the area bounded by the curve |x| + |y| = 1.

[Hint: The required region is bounded by lines x + y = 1, x– y = 1, – x + y = 1 and – x – y = 1].

Find the area bounded by curves {(x, y): y ≥ x² and y = |x|}.

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).

Using the method of integration find the area of the region bounded by lines:

2x + y = 4, 3x – 2y = 6 and x – 3y + 5 = 0

Find the area of the region {(x, y) : y² ≤ 4x, 4x² + 4y² ≤ 9}

Area bounded by the curve y = x3, the x-axis and the ordinates x = – 2 and x = 1 is

The area bounded by the curve y = x |x|, x-axis and the ordinates x = – 1 and x = 1 is given by

[Hint: y = x² if x > 0 and y = – x² if x < 0].

The area of the circle x² + y² = 16 exterior to the parabola y² = 6x is

The area bounded by the y-axis, y = cos x and y = sin x when is