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Indefinite Integrals

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  1. 151.If f() = _1^_10t1+t,dt, >0, then f(e^3)+f(e^-3) is equal to:
  2. 152.If [t] denotes the greatest integer t, then the value of _0^1[2x-|3x^2-5x+2|+1],dx is:
  3. 153.The integral e^3_e(2x)+5e^2_e(2x)e^4_ex+5e^3_ex-7e^2_ex,dx, x>0, is equal to (where c is a…
  4. 154.The value of the integral 2(6+4+2)√24+32+61-2,d is (where c is a constant of integration)
  5. 155.For x>0, if f(x) = _1^x(_et)/(1+t),dt, then f(e)+f(1e) is equal to
  6. 156.If I_m,n = _0^1 x^m-1(1-x)^n-1,dx, for m,n1, and _0^1x^m-1+x^n-1(1+x)^m+n,dx = ,I_m,n, R, …
  7. 157.The value of _n=1^100_n-1^n e^x-[x],dx, where [x] is the greatest integer x, is
  8. 158.The value of _-/2^/2(^2x)/(1+3^x),dx is
  9. 159.The value of the integral _0^|2x|,dx is ..........
  10. 160.The value of _-2^2|3x^2-3x-6|,dx is ..........
  11. 161.If I_n = _/4^/2^nx,dx, then:
  12. 162.The value of _-1^1 x^2,e^[x^3],dx, where [t] denotes the greatest integer t, is
  13. 163.Let f(x) be a differentiable function defined on [0,2], such that f'(x)=f'(2-x) for all x(…
  14. 164.The value of the integral _1^3[x^2-2x-2],dx, where [x] denotes the greatest integer less t…
  15. 165._x0_0^x^2 t,dtx^3 is equal to:
  16. 166.If _-a^a(|x|+|x-2|),dx=22 (a>2) and [x] denotes the greatest integer x, then _a^-a(x+[x]),…
  17. 167.The integral (2x-1)(2x-1)^2+5√4x^2-4x+6,dx is equal to (where c is a constant of integrati…
  18. 168.If f(x) = (5x^8+7x^6)/((x^2+1+2x^7)^2),dx, x0, f(0)=0 and f(1)=1K, then the value of K is …
  19. 169.For real numbers ,,,, if [(x^2-1)+^-1(x^2+1x)(x^4+3x^2+1)^-1(x^2+1x),dx = _e|^-1(x^2+1x)|+…
  20. 170.Let f(x) and g(x) be two functions satisfying f(x^2)+g(4-x)=4x^3 and g(4-x)+g(x)=0.
  21. 171.Let P(x) be a real polynomial of degree 3 which vanishes at x=-3.
  22. 172.Which of the following statements is correct for the function g(), for R, such that g() = …
  23. 173.Let f:RR be defined as f(x)=e^-x x.
  24. 174.If the integral _0^10[ 2 x]e^x-[x],dx= e^-1+ e^-1/2+, where ,, are integers and [x] denote…
  25. 175.Let I_n=_1^e x^19(|x|)^n,dx, where n N.
  26. 176.Let f:(0,2)R be defined as f(x)=_2(1+ x4).
  27. 177.If the normal to the curve y(x)=_0^x(2t^2-15t+10),dt at a point (a,b) is parallel to the l…
  28. 178.Let f:RR be a continuous function such that f(x)+f(x+1)=2, for all xR.
  29. 179.Consider the integral I=_0^10[x]e^[x]e^x-1,dx where [x] denotes the greatest integer less …
  30. 180.Let the domain of the function f(x)=_4(_5(_3(18x-x^2-77))) be (a,b).
  31. 181.The value of _n(1)/(n)_j=1^n((2j-1)+8n)/((2j-1)+4n) is equal to :
  32. 182.The value of the definite integral _-/4^/4dx(1+e^x x)(^4x+^4x) is equal to:
  33. 183.The value of the definite integral _/24^5/24dx1+[3]2x is
  34. 184.The value of the integral _-1^1(x+x^2+1)dx is:
  35. 185.If _0^100^2xe^x/,dx=()/(1+4^2), R, where [x] is the greatest integer less than or equal to…
  36. 186.The value of the integral _-1^1_e(√1-x+√1+x)dx is equal to :
  37. 187.If [x] denotes the greatest integer less than or equal to x, then the value of the integra…
  38. 188.If f:RR is given by f(x)=x+1, then the value of _n(1)/(n)[f(0)+f(5n)+f(10n)++f((5(n-1))/(n…
  39. 189.Let g(t)=_-/2^/2(()/(4)t+f(x))dx, where f(x)=_e(x+x^2+1), xR.
  40. 190.Let F:[3,5]R be a twice differentiable function on (3,5) such that F(x)=e^-x_3^x(3t^2+2t+4…
  41. 191.If _0^(3x)e^-^2x,dx=-e_0^1t,e^t,dt, then + is equal to _____ .
  42. 192.The value of _-/2^/21+^2x1+^ x,dx is
  43. 193.If x- x√8-2x,dx=a^-1( x+ xb)+c, where c is a constant of integration, then the ordered pai…
  44. 194.The integral dx[4](x-1)^3(x+2)^5 is equal to (where C is a constant of integration)
  45. 195.If ( x)/(^3x+^3x),dx=_e|1+ x|+_e|1- x+^2x|+^-1(2 x-1√3)+C, where C is constant of integrat…
  46. 196.If (dx)/((x^2+x+1)^2)=a^-1(2x+1√3)+b2x+1x^2+x+1+C, x>0, where C is the constant of integra…
  47. 197.If 2e^x+3e^-x4e^x+7e^-x,dx=114(ux+v_e(4e^x+7e^-x))+C, where C is a constant of integration…
  48. 198.Section B : Numerical Type Questions.
  49. 199.If x(x)=_5^x(3t^2-2'(t)),dt, x>-2, and (0)=4, then (2) is Answer: 4
  50. 200.If [x] is the greatest integer x, then 2_0^2( x2)x^[x],dx is equal to (where x=x-[x])