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Find the area under the given curves and given lines:
y = x2, x = 1, x = 2 and x-axis
We can see from the figure that the area of the region bounded by the curve y = x2 and the lines x = 1, x = 2 is shown by shaded region that is Area ADCBA.
Area of ADCBA =
⇒
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