Question : 1 Using integration, find the area bounded by the curve 4x2 + y2 = 36.
Answer: 18Ï€
Question : 2 The area bounded by the curve, y2 = 4x, y-axis, and y = 3 is represented as
Answer: 9/4
Question : 3Answer: 15/4
Solution Hint
Question : 4 Sketch the graph of y = x|x| and hence find the area bounded by this curve, X – axis and the ordinates x = -2 and x = 2, using integration.
Answer: 16/3
Solution Hint: [Hint: y = x2 if x > 0 and y = –x2 if x < 0]
Question 5: Using integration, find the area of the region enclosed between the circle x2 + y2 = 16 and the lines x = – 2 and x = 2.
Answer: 8√3+16Ï€/3
Question 6: Using integration, find the area bounded by the ellipse 9x2 +25y2 = 225, the line x = -2, x =2, and the x-axis.
Answer:
Question 7: Using integration find the area of the ellipse
Answer: 4√3 + 8Ï€/3
Question 8: Find the area of the region bounded by the curves x2 = y, y = x+2 and x-axis, using integration.
Answer: 5/6
Solution Hint:
Answer: π/3
Question 10: Using integration, find the area of the region bounded by the parabola y2 = 4ax and its latus rectum.
Answer: 8/3 a2
Question 11: Find the area bounded by the y-axis, y = cos x and y = sin x when
Answer: √2 - 1
Solution Hint
Answer: 4 Square unit
Solution Hint
Question : 13: Using integration find the area of region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1).
Answer: 3/2 Square Units
Question 14: Using integration find the area of region bounded by the triangle whose vertices
are (– 1, 0), (1, 3) and (3, 2).
Answer: 4 Square Units
Question 15: Using integration find the area of the triangular region whose sides have the equations y = 2x + 1, y = 3x + 1 and x = 4.
Answer: 8 Units
Question 16: If A1 denotes the area of region bounded by y2 = 4x, x = 1 and x-axis in the first quadrant and A2 denotes the area of region bounded by y2 = 4x, x = 4, find A1 : A2.
Answer: A1 4/3, A2 = 64/3, A1 : A2 =1:16
Question 17: Find the area of the region bounded by the curves y = x2 + 2, y = x, x = 0 and x = 3
Answer: 21/2
Solution Hint:
Question : 18: Sketch the graph of y = |x + 3| and evaluate
Answer: 9
Question : 19: Find the area enclosed by the parabola 4y = 3x2 and the line 2y = 3x +12
Answer: 27 Square Unit
Solution Hint:
Question : 20 : Using the method of integration find the area bounded by the curve |x| + |y| = 1
Answer: 2 Square units
Solution Hint
Answer:
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