Math Assignment Class XII Ch-8 | Applications of Integrations

 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 = 2

Answer: 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:  

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

Question 13: Find the area of the region bounded by y = sin(x), y = cos(x), x = 0, and x = π/4.

Answer: √2-1

Question 14: Find the area of the region enclosed between the curves y = sin(x) and y = cos(x) from x = π/4 to x = 3π/4.

Answer: 2 + √2

Question : 15: 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 16: 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 17: 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 18: 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 19: 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 : 20:  Sketch the graph of y = |x + 3| and evaluate     

Answer: 9

Question : 21: Find the area enclosed by the parabola 4y = 3x² and the line 2y = 3x +12

Answer: 27 Square Unit

Solution Hint:

Question : 22 :  Using the method of integration find the area bounded by the curve |x| + |y| = 1

Answer: 2 Square units

Solution Hint

Question : 23 : Find the area of the smaller region bounded by the ellipse  and the line  .

Answer:   

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