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Find the area of the region included between the parabola y2 = x and the line x + y = 2.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
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Draw a rough sketch of the region {(x, y) : y2 ≤ 5x, 5x2 + 5y2 ≤ 36} and find the area enclosed by the region using method of integration.
Concept: undefined >> undefined
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.
Concept: undefined >> undefined
Prove that the area in the first quadrant enclosed by the x-axis, the line x = \[\sqrt{3}y\] and the circle x2 + y2 = 4 is π/3.
Concept: undefined >> undefined
Find the area of the region bounded by \[y = \sqrt{x}, x = 2y + 3\] in the first quadrant and x-axis.
Concept: undefined >> undefined
Find the area common to the circle x2 + y2 = 16 a2 and the parabola y2 = 6 ax.
OR
Find the area of the region {(x, y) : y2 ≤ 6ax} and {(x, y) : x2 + y2 ≤ 16a2}.
Concept: undefined >> undefined
Find the area, lying above x-axis and included between the circle x2 + y2 = 8x and the parabola y2 = 4x.
Concept: undefined >> undefined
Find the area enclosed by the parabolas y = 5x2 and y = 2x2 + 9.
Concept: undefined >> undefined
Prove that the area common to the two parabolas y = 2x2 and y = x2 + 4 is \[\frac{32}{3}\] sq. units.
Concept: undefined >> undefined
Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4).
Concept: undefined >> undefined
Find the area of the region bounded by \[y = \sqrt{x}\] and y = x.
Concept: undefined >> undefined
Find the area of the region in the first quadrant enclosed by x-axis, the line y = \[\sqrt{3}x\] and the circle x2 + y2 = 16.
Concept: undefined >> undefined
Find the area of the region bounded by the parabola y2 = 2x + 1 and the line x − y − 1 = 0.
Concept: undefined >> undefined
Find the area of the region bounded by the curves y = x − 1 and (y − 1)2 = 4 (x + 1).
Concept: undefined >> undefined
Find the area enclosed by the curve \[y = - x^2\] and the straight line x + y + 2 = 0.
Concept: undefined >> undefined
Find the area bounded by the parabola y = 2 − x2 and the straight line y + x = 0.
Concept: undefined >> undefined
Using the method of integration, find the area of the region bounded by the following lines:
3x − y − 3 = 0, 2x + y − 12 = 0, x − 2y − 1 = 0.
Concept: undefined >> undefined
Sketch the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 1. Also, find the area of this region.
Concept: undefined >> undefined
Find the area bounded by the curves x = y2 and x = 3 − 2y2.
Concept: undefined >> undefined
