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Indefinite Integrals

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  1. 301.Let f: (-1,1) R be a continuous function.
  2. 302.For x>0, let f(x) = _1^x t1+t,dt.
  3. 303.The integral (1+x-1x)e^x+1x,dx is equal to
  4. 304.The integral ^2x^2x(^3x+^3x)^2,dx is equal to:
  5. 305.The integral x^-1(1-x^21+x^2)dx (x>0) is equal to:
  6. 306.^8x-^8x1-2^2x^2x,dx is equal to:
  7. 307.If m is a non-zero number and x^5m-1+2x^4m-1(x^2m+x^m+1)^3,dx = f(x)+c, then f(x) is:
  8. 308.The integral _0^ [1+4^2x2]^1/2dx equals: *(interpreting garbled OCR as _0^ √1+4^2(x/2),dx …
  9. 309.Let function F be defined as F(x) = _1^x e^tt,dt, x>0 then the value of the integral _1^x …
  10. 310.If for a continuous function f(x), _-^t (f(x)+x),dx = ^2-t^2, for all t -, then f(-3) is e…
  11. 311.If [,] denotes the greatest integer function, then the integral _0^ [ x],dx is equal to:
  12. 312.If for n 1, P_n = _1^e ( x)^n,dx, then P_10-90P_8 is equal to:
  13. 313.The integral _0^1/2 (1+2x)1+4x^2,dx, equals:
  14. 314.If f(x),dx = (x), then x^5 f(x^3),dx is equal to
  15. 315.If the integral 8x+1 2x- 2x,dx = A 8x+k where k is an arbitrary constant, then A is equal …
  16. 316.The integral x,dx√2-x^2+2-x^2 equals:
  17. 317.If x^2-x+1x^2+1e^^-1x,dx = A(x)e^^-1x+C, then A(x) is equal to:
  18. 318.If dxx+x^7 = p(x) then x^6x+x^7,dx is equal to:
  19. 319.The intercepts on x-axis made by tangents to the curve, y = _0^x |t|,dt, x R, which are pa…
  20. 320.Statement-1: The value of the integral _/6^/3 dx1+ x is equal to /6 Statement-2: _a^b f(x)…
  21. 321.For 0 x 2, the value of _0^^2x ^-1( t),dt + _0^^2x ^-1( t),dt equals:
  22. 322.The integral _7/4^7/3 ^2x,dx is equal to:
  23. 323.If x = _0^y dt√1+t^2, then d^2ydx^2 is equal to:
  24. 324.If the 5 x x-2,dx = x + a| x-2 x|+k, then a is equal to:
  25. 325.If f(x) = x^2+^2x1+x^2^2x,dx and f(0)=0, then f(1) equals:
  26. 326.The integral of x^2-xx^3-x^2+x-1 w.r.t.
  27. 327.Let f(x) be an indefinite integral of ^3x.
  28. 328.If g(x) = _0^x 4t,dt, then g(x+) equals:
  29. 329.If [x] is the greatest integer x, then the value of the integral _-0.9^0.9([x^2]+(2-x2+x))…
  30. 330.The value of the integral _0^0.9 [x-2[x]],dx, where [.] denotes the greatest integer funct…
  31. 331.If ddxG(x) = e^ xx, x (0,/2), then _1/4^1/2 2xe^( x^2),dx is equal to:
  32. 332.If e^t f(t),dt = x - x x - x^22, for all x R-0, then the value of f(6) is:
  33. 333.f(x) = dx^6x is a polynomial of degree
  34. 334.Let [.] denote the greatest integer function then the value of _0^1.5 x[x^2],dx is:
  35. 335.The value of _0^1 8(1+x)1+x^2,dx is:
  36. 336.Let p(x) be a function defined on R such that p'(x) = p'(1-x), for all x [0,1], p(0)=1 and…
  37. 337._0^ [ x],dx, where [.] denotes the greatest integer function, is equal to:
  38. 338.The value of √2 x,dx(x-4) is:
  39. 339.Let I = _0^1 x x,dx and J = _0^1 x x,dx.
  40. 340.dx x+√3 x equals:
  41. 341.The solution for x of the equation _√2^x dttt^2-1 = 2 is:
  42. 342.Let F(x) = f(x)+f(1x), where f(x) = _1^x t1+t,dt.
  43. 343.The value of _1^a [x]f'(x),dx, a>1 where [x] denotes the greatest integer not exceeding x …
  44. 344._-3/2^-/2 [(x+)^3+^2(x+3)],dx is equal to:
  45. 345._0^ xf( x),dx is equal to:
  46. 346.The value of integral, _3^6 x√9-x+ x,dx is:
  47. 347.( x-1)1+( x)^2,dx is equal to: *(reading the OCR'd numerator/denominator as ( x-1)^2[1+( x…
  48. 348.The value of _-^ ^2x1+a^x,dx, a>0, is:
  49. 349.If I_1 = _0^1 2^x^2,dx, I_2 = _0^1 2^x^3,dx, I_3 = _1^2 2^x^2,dx and I_4 = _1^2 2^x^3,dx, …
  50. 350.Let f: R R be a differentiable function having f(2)=6, f'(2)=148.