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Definite Integration

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  1. 201.[_0^ 6e^3 x+6 e^2 x+11 e^x+6 d x=]
  2. 202.If _0^1 1(5+2 x-2 x^2)(1+e^(2-4 x)) d x=(1)/() _e((+1)/()), , >0, then ^4-^4 is equal to :
  3. 203.[_3 2 4^3 3 4 48 9 - 4x^2 dx ] is equal to :
  4. 204._n (3)/(n)4+(2+(1)/(n))^2+(2+(2)/(n))^2++(3-(1)/(n))^2 is equal to :
  5. 205.If [t] denotes the greatest integer [ t], then the value of [3(e - 1) e_1^2 x^2e^[x] + [x^…
  6. 206.Let >0.
  7. 207.If (x)=1x _()/(4)^x(4 √2 t-3 ^(t)) d t, x>0, then ^(()/(4)) is equal to :
  8. 208.The value of [_()/(3)^()/(2) ((2+3 x))/( x(1+ x)) d x] is equal to :
  9. 209.Let f(x) be a function satisfying [f(x)+f(-x)=^2, x R].
  10. 210.[ _n (2^(1)/(2)-2^(1)/(3))(2^(1)/(2)-2^(1)/(5)) .
  11. 211.Let [5 f(x)+4 f((1)/(x))=(1)/(x)+3, x > 0].
  12. 212.If _0^()/(3) ^4 x ~d x=a +b √3, where a and b are rational numbers, then 9 a+8 b is equal …
  13. 213.The value of _0^1(2 x^3-3 x^2-x+1)^(1)/(3) ~d x is equal to :
  14. 214.The value of the integral _0^ / 4 x ~d x ^4(2 x)+ ^4(2 x) equals :
  15. 215.If _0^1 1√3+x+√1+x ~d x=a+b √2+c √3, where a, b, c are rational numbers, then 2 a+3 ~b-4 c…
  16. 216.If (a, b) be the orthocentre of the triangle whose vertices are (1,2),(2,3) and (3,1), and…
  17. 217.[ _x 2 ( 1 ( x - 2 )^2_x^3^( 2 )^3 ( t^1 3 )dt )] is equal to
  18. 218.If the value of the integral [_-()/(2)^()/(2)((x^2 x)/(1+^x)+1+ ^2 x1+e^ x^2123) d x=()/(4…
  19. 219.Let y=f(x) be a thrice differentiable function in (-5,5).
  20. 220.Let a and b be real constants such that the function f defined by [f(x)=[arrayll x^2+3 x+a…
  21. 221.Let [f: R R] be defined as f(x)=a e^2 x+b e^x+c x.
  22. 222.The value of [ _n _k=1^n (n^3)/((n^2+k^2)(n^2+3 k^2))] is :
  23. 223.Let [f, g:(0, ) R] be two functions defined by [f(x)=_-x^x(|t|-t^2) e^-t^2 d t] and [g(x)=…
  24. 224.Let [f(x)=_0^x(t+ (1-e^t)) d t, x R].
  25. 225.If the value of the integral [_-1^1 ( x)/(1+3^x) d x] is [(2)/()].Then, a value of [] is
  26. 226.The integral [_0^ / 4 (136 x)/(3 x+5 x) ~d x] is equal to :
  27. 227.The value of [_-^ (2 y(1+ y))/(1+ ^2 y) d y] is :
  28. 228.[_0^ / 4 ( ^2 x ^2 x)/(( ^3 x+ ^3 x)^2) d x is equal to ]
  29. 229.Let [_^ _e 4 d xe^x-1=()/(6)].
  30. 230.The value of [k N] for which the integral [I_n=_0^1(1-x^k)^n d x, n N], satisfies 147 I_20…
  31. 231.The integral [_1 / 4^3 / 4 (2 ^-1 (1-x)/(1+x)) d x] is equal to
  32. 232.[ _x ()/(2)(_x^3^( / 2)^3( (2 t^1 / 3)+ (t^1 / 3)) d t(x-()/(2))^2)] is equal to
  33. 233.The value of the integral [_-1^2 _e(x+x^2+1) d x] is
  34. 234.If I=_0^()/(2) ^(3)/(2) x ^(3)/(2) x+ ^(3)/(2) x ~d x, then _0^2I (x x x)/( ^4 x+ ^4 x) ~d…
  35. 235.The value of _e^2^e^4 (1)/(x)(e^(( _e x)^2+1)^-1e^(( _e x)^2+1)^-1+e^((6- _e x)^2+1)^-1) d…
  36. 236.If I(m, n)=_0^1 x^m-1(1-x)^n-1 d x, m, n>0, then I(9,14)+I(10,13) is
  37. 237.Let f be a real valued continuous function defined on the positive real axis such that g(x…
  38. 238.If _-()/(2)^()/(2) (96 x^2 ^2 x)/((1+e^x)) d x=( ^2+), , Z, then (+)^2 equals
  39. 239.Let f(x)=_0^x t(t^2-9 t+20) dt, 1 x 5.
  40. 240.Let f:[1, ) [2, ) be a differentiable function.
  41. 241.4 _0^1(1√3+x^2+√1+x^2) d x-3 _e(√3) is equal to :
  42. 242.The integral _0^ (8 x d x)/(4 ^2 x+ ^2 x) is equal to
  43. 243.Let the domain of the function f(x)= _2 _4 _6(3+4 x-x^2) be (a, b).
  44. 244.Let f(x)+2 f((1)/(x))=x^2+5 and 2 g(x)-3 g((1)/(2))=x, x>0.
  45. 245.The value of _-1^1 (1+|x|-x) e^x+(|x|-x) e^-xe^x+e^-x d x is equal to
  46. 246.The integral _0^ ((x+3) x)/(1+3 ^2 x) d x is equal to