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Area Under Curves

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  1. 51.The area of the region : [R = (x,y):5x^2 y 2x^2 + 9 ] is :
  2. 52.The area (in sq.
  3. 53.The area (in sq.
  4. 54.The area (in sq.
  5. 55.The area (in sq.
  6. 56.Let f:R R be a function such that f(x)+3f(( )/(2)-x)= x,x R.
  7. 57.If the area of the region bounded by 16x^2 - 9y^2 = 144 and 8x - 3y = 24 is A, then 3(A + …
  8. 58.Let the area of the region bounded by the curve y= x, x, lines x=0, x=(3 )/(2), and the x-…
  9. 59.Let the area of the bounded region (x,y):0 9x y^2,y 3x-6 be A.
  10. 60.If the area of the region (x,y):|x-5| y 4x is A, then 3A is equal to _________.
  11. 61.The area of the region bounded by the curve y= |x|, x|x-2|, the x-axis and the lines x=-2 …
  12. 62.If the area of the region (x,y):|4-x^2| y x^2,y 4,x 0 is (80√2 - ), , N, then + is equal t…
  13. 63.If the area of the larger portion bounded between the curves x^2+y^2=25 and y=|x-1| is (1)…
  14. 64.Let the area of the region enclosed by the curve [y= x, x] and the x axis between [x=-] to…
  15. 65.The area of the region enclosed by the parabolas y=x^2-5 x and y=7 x-x^2 is ________.
  16. 66.Three points O(0,0),P(a,a^2),Q(-b,b^2),a>0,b>0, are on the parabola y=x^2.
  17. 67.The sum of squares of all possible values of k, for which area of the region bounded by th…
  18. 68.The area of the region enclosed by the parabola (y-2)^2=x-1, the line x-2 y+4=0 and the po…
  19. 69.Let the area of the region (x,y):0 x 3,0 y minx^2+2,2x+2 be A.
  20. 70.The area (in sq.
  21. 71.If the points of intersection of two distinct conics x^2+y^2=4 b and [(x^2)/(16)+(y^2)/(b^…
  22. 72.If the area of the region (x,y):0 y min2x,6x-x^2 is A, then 12A is equal to ________.
  23. 73.Let the area of the region (x,y):x-2y+4 0,x+2y^2 0,x+4y^2 8,y 0 be (m)/(n), where m and n …
  24. 74.If the area bounded by the curve 2 y^2=3 x, lines x+y=3, y=0 and outside the circle (x-3)^…
  25. 75.If A is the area in the first quadrant enclosed by the curve C:2x^2-y+1=0, the tangent to …
  26. 76.If the area of the region (x,y):|x^2-2| y x is A, then 6A+16√2 is equal to __________.
  27. 77.Let y = p(x) be the parabola passing through the points ( - 1,0),(0,1) and (1,0).
  28. 78.Let the area enclosed by the lines x+y=2,y=0,x=0 and the curve f(x)=minx^2+(3)/(4),1+[x] w…
  29. 79.If the area of the region S=(x,y):2y-y^2 x^2 2y,x y is equal to (n+2)/(n+1)-( )/(n-1), the…
  30. 80.Let the area of the region (x,y):|2x-1| y |x^2-x|,0 x 1 be A.
  31. 81.Let A be the area of the region (x,y):y x^2,y (1-x)^2,y 2x(1-x).
  32. 82.Let f : R R be a function such that f(x) + 3f(2 - x) = x, x R.
  33. 83.The area of the region, inside the ellipse x^2 + 4y^2 = 4 and outside the region bounded b…
  34. 84.If the area of the region (x,y) : 1 - 2x y 4 - x^2, x 0, y 0 is , where , N, (,) = 1, then…
  35. 85.Let the line x = -1 divide the area of the region (x,y) : 1 + x^2 y 3-x in the ratio m:n, …
  36. 86.The area of the region A = (x,y) : 4x^2+y^2 8, y^2 4x is:
  37. 87.Let f() denote the area of the region bounded by x=0, x=1, y^2=x and y = | x - 5| - |1- x|…
  38. 88.The area of the region bounded by the curves x+3y^2=0 and x+4y^2=1 is equal to:
  39. 89.Let e be the base of natural logarithm and let f : 1,2,3,4 1,e,e^2,e^3 and g : 1,e,e^2,e^3…
  40. 90.The area of the region A = (x,y) : 0 y 6-x, y^2 4x-3, x 0 is:
  41. 91.The area of the region enclosed by the curves y = x^2-4x+4 and y^2 = 16-8x is:
  42. 92.If the area of the region (x,y) : -1 x 1, 0 y a+e^|x|-e^-x, a>0 is e+8+1e, then the value …
  43. 93.Let the area of the region (x,y) : 2y x^23+3, y+|x|3, y |x-1| be A.
  44. 94.If the area of the larger portion bounded between the curves x^2+y^2=25 and y=|x-1| is 14(…
  45. 95.Let A_1 be the area of the region bounded by the curves y= x, y= x and the y-axis in the f…
  46. 96.The area bounded by the curve y = ||x-1|-2| and the x-axis is ________.
  47. 97.The graph of sine and cosine functions intersect each other at a number of points, and bet…
  48. 98.The area of the region R = (x,y) : 5x^2 y 2x^2+9 is:
  49. 99.If the area of the triangle formed by the positive x-axis, the normal, and the tangent to …
  50. 100.The area (in sq.