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Definite Integration

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  1. 101.If the integral 525 _0^( )/(2) 2x ^(11)/(2)x(1+Cos^(5)/(2)x)^(1)/(2)dx is equal to (n√2-64…
  2. 102.Let S=(-1,) and f:S R be defined as f(x)= _-1^x(e^t-1)^11(2t-1)^5(t-2)^7(t-3)^12(2t-10)^61…
  3. 103.Let f:R R be a function defined by f(x)=4^x4^x+2 and M= _f(a)^f(1-a)x ^4(x(1-x))dx,N= _f(a…
  4. 104.The value of 9 _0^9[(10x)/(x+1)]dx, where [t] denotes the greatest integer less than or eq…
  5. 105.Let the slope of the line 45x+5y+3=0 be 27r_1+9r_22 for some r_1,r_2 R.
  6. 106.If _( )/(6)^( )/(3)√1- 2xdx= + √2+ √3, where , and are rational numbers, then 3 +4 - is eq…
  7. 107.Let f(x)= _0^xg(t) _e((1-t)/(1+t))dt, where g is a continuous odd function.
  8. 108.Let f_n= _0^( )/(2)( _k=1^n ^k-1x)( _k=1^n(2k-1) ^k-1x) xdx,n N.
  9. 109.Let for x R,S_0(x)=x,S_k(x)=C_kx+k _x^0S_k-1(t)dt, where C_0=1,C_k=1- _1^0S_k-1(x)dx,k=1,2…
  10. 110.If _-0.15^0.15|100x^2-1|dx=(k)/(3000), then k is equal to ___________.
  11. 111.For m,n>0, let (m,n)= _0^2t^m(1+3t)^ndt.
  12. 112.Let [t] denote the greatest integer function.
  13. 113.Let [t] denote the greatest integer t.
  14. 114.Let f(x)=x(1+x^n)^(1)/(n),x R--1,n N,n>2.
  15. 115.[I_n = _0^ /4 ^nx,dx ] then [, _n ,n[ I_n + I_n + 2 ]] equals
  16. 116.[_ - ^ 2x( 1 + x ) 1 + ^2x dx] is
  17. 117.If y=f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 …
  18. 118.[ _n 1 + 2^4 + 3^4 + ....
  19. 119.The value of [ _x 0 _0^x^2 ^2tdt xsinx] is
  20. 120.[ Lim_n _r = 1^n 1 ne^r n ] is
  21. 121.Let [f:R R] be a differentiable function having [f( 2 ) = 6], [f'( 2 ) = ( 1 48 )].
  22. 122.The value of [_ - ^ ^2 1 + a^xdx,,,a > 0, ] is
  23. 123.Let [F( x ) = f( x ) + f( 1 x ),] where [f( x ) = _l^x t 1 + tdt, ] Then F(e) equals
  24. 124.The integral [_0^ 1 + 4 ^2x 2 - 4 x 2 1mu dx] equals:
  25. 125.If [2_0^1 ^ - 1xdx = _0^1 ^ - 1 ( 1 - x + x^2 )dx,] then [_0^1 ^ - 1 ( 1 - x + x^2 )dx] is…
  26. 126.If [ _n ,,1^a + 2^a + ......
  27. 127.The value of [_ - /2^ /2 ^2x 1 + 2^x dx] is
  28. 128.If [I_1 = _0^1 e^ - x ^2x 1mu dx;] [I_2 = _0^1 e^ - x^2 ^2x 1mu dx] and [I_3 = _0^1 e^ - x…
  29. 129.The value of the integral [_ - 2^ 2 ^4 x( 1 + ( 2 + x 2 - x ) )dx] is :
  30. 130.The integral [_ /6^ /3 ^2/3 x ec^4/3xdx] is equal to :
  31. 131.If [_0^x , ]f(t) dt = x2 + [_x^1 , ] t2f(t) dt then f '[( 1 2 )] is -
  32. 132.Let [ I = _a^b ( x^4 - 2x^2 ) dx.] If I is minimum then the ordered pair (a, b) is -
  33. 133.The integral [_ /6^ /4 dx 2x( ^5x + ^5x ) ] equals :
  34. 134.The value of the integral [_ - 2^2 ^2x [ x ] + 1 2 ,dx] (where [x] denotes the greatest in…
  35. 135.A value of [ ] such that [_ ^ + 1 dx ( x + )( x + + 1 ) = _e( 9 8 )] is :
  36. 136.Let f : R [ ] R be a continuously differentiable function such that f(2) = 6 and f'(2) = […
  37. 137.If [_0^ 2 x x + ecx dx] = m([ ] + n), then m.n is equal to
  38. 138.The integral [_1^e ( x e )^2x - ( e x )^x ,] loge x dx is equal to :
  39. 139.Let f and g be continuous functions on [0, a] such that f(x) = f(a -- x) and g(x) + g(a --…
  40. 140.If [f(x) = 2 - x x 2 + x x] and g(x) = logex, (x > 0) then the value of integral [_ - 4^ 4…
  41. 141.If f : R [ ] R is a differentiable function and f(2) = 6, then [ _x 2 _6^f( x ) 2tdt ( x -…
  42. 142.The value of the integral [_0^1 x ^ - 1(1 - x^2 + x^4)dx ] is :-
  43. 143.The value of [_0^ /2 ^3x x + xdx ] is
  44. 144.Let f be a differentiable function from R to R such that [| f( x ) - f( y ) | 2| x - y |^3…
  45. 145.If the value of the integral [_0^1 2 x^2 ( 1 - x^2 )^3 2 dx] is [k 6], then k is equal to …
  46. 146.Suppose f(x) is a polynomial of degree four, having critical points at --1, 0, 1.
  47. 147.The integral [_ 6^ 3 ^3x. ^23x( 2 ^2x. ^23x + 3 x. 6x )dx ] is equal to:
  48. 148.The integral [_1^2 e^x.x^x( 2 + _ex ) dx] equals :
  49. 149.If I1 = [_0^1 ( 1 - x^50 )^100 dx] and I2 = [_0^1 ( 1 - x^50 )^101 dx] such that I2 = [ ]I…
  50. 150.If [ ]1 and [ ]2 be respectively the smallest and the largest values of [ ] in (0, 2[ ]) -…