Mathematics Assignment on
applications of integral Class XII
Important and extra questions on Applications of Integral for class XII, This assignment is strictly based on previous years CBSE question papers.
Question : 1 Using integration, find the area bounded by the curve 4x2 + y2 = 36.Answer: 18π
Question : 2 The area bounded by the curve, y2 = 4x, y-axis,
and y = 3 is represented as
Answer: 9/4
Question : 3 Find Area bounded by the curve y = x3, the x-axis and the ordinates x = –2 and x = 1 Answer: 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+16π/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 
, included between the lines x = -2 and x = 2Answer: 4√3 + 8π/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: dx+\int_{-1}^{0}x^{2}dx)
Question 9: Using integration, find the area of the region bounded by
the line y =√3x , the curve y = 
and y-axis
in the first quadrant.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
Question 12: Find the area bounded by the curve y = sin x between x = 0
and x = 2π
Answer: 4 Square unit
Solution Hint
Or
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 verticesare (– 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 = 3Answer: 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
Question : 21 : Find the area of the smaller region bounded by the ellipse 
and the line
.
Answer: }{2})
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