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Area Under Curves

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  1. 1.Let f:(1,) R be a function defined as f(x)=(x-1)/(x+1).
  2. 2.The area of the region (x,y):x^2-8x y -x is :
  3. 3.The area of the region (x,y):0 y 6-x,y^2 4x-3,x 0 is :
  4. 4.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 1,(…
  5. 5.The area of the region R=(x,y):xy 27,1 y x^2 is equal to :
  6. 6.The area of the region bounded by the curves x+3 y^2=0 and x+4 y^2=1 is equal to :
  7. 7.The area of the region (x,y):y -|x|,y |x x|,y 0 is:
  8. 8.Let P_1 : y = 4x^2 and P_2 : y = x^2 + 27 be two parabolas.
  9. 9.The area of the region R=(x,y):xy 8,1 y x^2,x 0 is
  10. 10.Let f( ) denote the area of the region in the first quadrant bounded by x=0,x=1,y^2=x and …
  11. 11.Let A_1 be the bounded area enclosed by the curves y=x^2+2,x+y=8 and y-axis that lies in t…
  12. 12.The area of the region enclosed between the circles x^2+y^2=4 and x^2+(y-2)^2=4 is:
  13. 13.The area of the region A=(x,y):4x^2+y^2 8 and y^2 4x is:
  14. 14.Let the line x=-1 divide the area of the region (x,y):1+x^2 y 3-x in the ratio m:n,gcd(m,n…
  15. 15.If the area of the region (x,y):1-2x y 4-x^2,, x 0,, y 0 is ( )/( ), , N,gcd( , )=1, then …
  16. 16.The area of the region, inside the ellipse x^2+4 y^2=4 and outside the region bounded by t…
  17. 17.If the area of the region (x,y):1+x^2 y minx+7,11-3x is A, then 3A is equal to :
  18. 18.If the area of the region bounded by the curves y=4-(x^2)/(4) and y=(x-4)/(2) is equal to …
  19. 19.Let f:[0,) R be a differentiable function such that f(x)=1-2x+ _x^0e^x-tf(t)dt for all x […
  20. 20.The area of the region (x,y):|x-y| y 4x is
  21. 21.Let the area enclosed between the curves |y|=1-x^2 and x^2+y^2=1 be .
  22. 22.Let the area of the region (x,y):2y x^2+3,y+|x| 3,y |x-1| be A.
  23. 23.The area of the region bounded by the curves x(1+y^2)=1 and y^2=2x is:
  24. 24.The area (in sq.
  25. 25.The area of the region enclosed by the curves y=e^x,y=|e^x-1| and y-axis is :
  26. 26.The area of the region (x,y):x^2+4x+2 y |x+2| is equal to
  27. 27.If the area of the region (x,y):-1 x 1,0 y a+e^|x|-e^-x,a>0 is e^2+8e+1e, then the value o…
  28. 28.The area of the region enclosed by the curves y=x^2-4 x+4 and y^2=16-8 x is :
  29. 29.The area of the region, inside the circle (x-2√3)^2+y^2=12 and outside the parabola y^2=2√…
  30. 30.The area (in square units) of the region enclosed by the ellipse x^2+3 y^2=18 in the first…
  31. 31.The parabola y^2=4 x divides the area of the circle x^2+y^2=5 in two parts.
  32. 32.The area of the region in the first quadrant inside the circle x^2+y^2=8 and outside the p…
  33. 33.If the area of the region (x,y):ax^2 y (1)/(x),1 x 2,0<a<1 is ( _e2)-(1)/(7) then the valu…
  34. 34.Let the area of the region enclosed by the curves y=3 x, 2 y=27-3 x and [y=3 x-x x] be A.
  35. 35.The area (in sq.
  36. 36.One of the points of intersection of the curves y=1+3x-2x^2 and y=(1)/(x) is ((1)/(2),2).
  37. 37.The area enclosed by the curves x y+4 y=16 and x+y=6 is equal to :
  38. 38.The area of the region enclosed by the parabolas y=4 x-x^2 and 3 y=(x-4)^2 is equal to :
  39. 39.The area of the region (x,y):y^2 4x,x0,x 3 is
  40. 40.The area (in square units) of the region bounded by the parabola y^2=4(x-2) and the line y…
  41. 41.The area of the region (x,y):x^2 y |x^2-4|,y 1 is
  42. 42.The area of the region enclosed by the curve f(x)=max x, x,- x and the x-axis is
  43. 43.The area of the region enclosed by the curve y=x^3 and its tangent at the point (-1,-1) is…
  44. 44.Area of the region (x,y):x^2+(y-2)^2 4,x^2 2y is
  45. 45.The area of the region (x,y):x^2 y 8-x^2,y 7 is :
  46. 46.The area bounded by the curves y=|x-1|+|x-2| and y=3 is equal to :
  47. 47.The area of the region given by [ (x,y):xy 8,1 y x^2 ] is :
  48. 48.Let q be the maximum integral value of p in [0,10] for which the roots of the equation x^2…
  49. 49.The area (in sq.
  50. 50.The area bounded by the curve 4y2 = x2(4 - x)(x - 2) is equal to :