Question 1:Find the area under the given curves and given lines: (i) y = x 2 , x = 1, x = 2 and x-axis (ii) y = x 4 , x = 1, x = 5 and x-axis
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Question 2:Find the area between the curves y = x and y = x 2 .
Question 3:Find the area of the region lying in the first quadrant and bounded by y = 4x 2 , x = 0, y = 1 and y = 4.
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Question 4:Sketch the graph of y = x ✢ 3 and evaluate 0 6 3 ✣ ✤ ✥ x dx .
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Question 5:Find the area bounded by the curve y = sin x between x = 0 and x = 2.
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Question 6:Find the area enclosed between the parabola y 2 = 4ax and the line y = mx.
Question 7:Find the area enclosed by the parabola 4y = 3x 2 and the line 2y = 3x + 12.
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Question 8:Find the area of the smaller region bounded by the ellipse 2 2 1 9 4 x y and the line 1 3 2 x y ✩ ✪ .
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Question 9:Find the area of the smaller region bounded by the ellipse 2 2 2 2 1 x y a b ✫ ✬ and the line 1 x y a b ✩ ✪ .
Question 10:Find the area of the region enclosed by the parabola x 2 = y, the line y = x + 2 and the x-axis.
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Question 11: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
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Question 12:Find the area bounded by curves {(x, y) : y x 2 and y = | x |}.
1. Find the area under the given curves and giv
Question 13: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).
Question 14: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
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Question 15:Find the area of the region {(x, y) : y 2 4x, 4x 2 + 4y 2 9} Choose the correct answer in the following Exercises from 16 to 20
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Question 16:Area bounded by the curve y = x 3 , the x-axis and the ordinates x = – 2 and x = 1 is (A) – 9 (B) 15 4(C) 15 4 (D) 17 4
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Question 17:The area bounded by the curve y = x | x | , x-axis and the ordinates x = – 1 and x = 1 is given by (A) 0 (B) 1 3 (C) 2 3 (D) 4 3 [Hint : y = x 2 if x > 0 and y = – x 2 if x < 0].
Question 18:The area of the circle x 2 + y 2 = 16 exterior to the parabola y 2 = 6x is (A) 4 (4 3) 3 (B) 4 (4 3) 3 (C) 4 (8 3) 3 (D) 4 (8 3) 3
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Question 19:The area bounded by the y-axis, y = cos x and y = sin x when 0 2 x is (A) 2 ( 2 1) (B) 2 1 (C) 2 1 (D
