Home
Class 12
MATHS
If I1=int0^1 2^(x^2)dx , I2=int0^1 2^(x^...

If `I_1=int_0^1 2^(x^2)dx , I_2=int_0^1 2^(x^3) dx , I_3= int_1^2 2^(x^2) dx , I_4=int_1^2 2^(x^3)dx` then

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE PUBLICATION|Exercise Jee Advanced (Single|1 Videos

  • INTRODUCTION TO VECTORS

    CENGAGE PUBLICATION|Exercise TRUE OR FALSE|1 Videos

Similar Questions

Explore conceptually related problems

int_(1)^(4)3x^(2)dx

int_(0)^(1)2^(2-3x)dx

Find int_0^2(x^2+1)dx

Consider I_1=int_0^(pi//4)e^(x^2)dx ,I_2=int_0^(pi//4)e^x dx ,I_3=int_0^(pi//4)e^(x^2)cosxdx , I_4=int_0^(pi//4)e^(x^2)sinxdx . STATEMENT 1 : I_2> I_1> I_3> I_4 STATEMENT 2 : For x in (0,1),x > x^2a n dsinx >cosx .

If I_I=int_0^(pi//2)cos(sinx)dx ,I_2=int_0^(pi/2)sin(cosx)dx \ ,a n d \ I_3=int_0^(pi/2)cosx dx , then find the order in which the values I_1,I_2,I_3, exist.

if int_0^1 f(x)dx=1,int_0^1 xf(x)dx=a and int_0^1 x^2f(x)dx=a^2 , then int_0^1(a-x)^2f(x)dx is equal to

I_1=int_0^(pi/2)(sinx-cosx)/(1+sinxcosx)dx ,I_2=int_0^(2pi)cos^6xdx ,I_3=int_(pi/2)^(pi/2)sin^3xdx ,I_4=int_0^1 1n(1/x-1)dxdotT h e n I_2=I_3=I_4=0,I_1!=0 I_1=I_2=I_3=0,I_4!=0 I_1=I_2=I_3=0,I_4!=0 I_1=I_4=I_3=0,I_2!=0

The number of positive continuous f(x) defined in [0,1] for with I_(1)=int_(0)^(1)f(x)dx=1,I_(2)=int_(0)^(1)xf(x)dx=a , I_(3)=int_(0)^(1)x^(2)f(x)dx=a^(2) is /are

The numbers of possible continuous f(x) defined in [0,1] for which I_1=int_0^1f(x)dx=1,I_2=int_0^1xf(x)dx-a ,I_3=int_0^1x^2f(x)dx=a^2i s//a r e 1 (b) oo (c) 2 (d) 0

If I_1=int_0^(pi//2)(cos^2x)/(1+cos^2x)dx , I_2=int_0^(pi//2)(sin^2x)/(1+sin^2x)dx and I_3=int_0^(pi//2)(1+2cos^2xsin^2x)/(4+2cos^2xsin^2x)dx , then (a) I_1=I_2 > I_3 (b) I_3> I_1=I_2 (c) I_1=I_2=I_3 (d) none of these

CENGAGE PUBLICATION-INTEGRALS-All Questions
  1. If int0^x[x]dx=int0^([x])xdx , then prove that either x is purely fr...

    Text Solution

    |

  2. Show that: int0^(pi//2)f(sin2x)sinxdx=sqrt(2)int0^(pi//4)f(cos2x)co...

    Text Solution

    |

  3. If I1=int0^1 2^(x^2)dx , I2=int0^1 2^(x^3) dx , I3= int1^2 2^(x^2) dx ...

    Text Solution

    |

  4. If af(x)+bf((1)/(x))=(1)/(x)-5,x ne 0,a ne b, then overset(2)underset(...

    Text Solution

    |

  5. Find the mistake in the following evaluation of the integral I=int0^pi...

    Text Solution

    |

  6. Find the value of int(-1)^1d/(dx)(tan^(-1)(1/x))dx

    Text Solution

    |

  7. The value of int2^3(sqrt(x))/(sqrt(5-x)+sqrt(x))dx is

    Text Solution

    |

  8. The value of int(-2)^2|1-x^2|dx is

    Text Solution

    |

  9. If II=int0^(pi//2)cos(sinx)dx ,I2=int0^(pi/2)sin(cosx)dx \ ,a n d \ I3...

    Text Solution

    |

  10. The integral int0^(1. 5)[x^2]dx ,w h e r e[dot] denotoes the greatest ...

    Text Solution

    |

  11. Evaluate the following limit: lim(nto oo)(sum(r=1)^(n) sqrt(r)sum(r=...

    Text Solution

    |

  12. value of underset(nrarrinfty)lim((n !)/n^n)^(1/n),where n inN is equal...

    Text Solution

    |

  13. If the value of the definite integral int0^1 "^(207)C7x^(200)(1-x)^7dx...

    Text Solution

    |

  14. Evaluate: int(-1)^0(dx)/(x^2+2x+2)

    Text Solution

    |

  15. If fa n dg are continuous function on [0,a] satisfying f(x)=f(a-x)a ...

    Text Solution

    |

  16. If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int(-1)^1...

    Text Solution

    |

  17. Evaluate: int0^pie^(|cosx|)(2sin(1/2cosx)+3cos(1/2cosx))sinxdxdot

    Text Solution

    |

  18. Evaluate: inta^b x^3dx

    Text Solution

    |

  19. Find the value of int(-pi/3)^(pi/3)(pi+4x^3)/(2-cos(|x|+pi/3))dx

    Text Solution

    |

  20. Evaluate: ("lim")(n rarr oo)(1/(sqrt(4n^2-1))+1/(sqrt(4n^2-2^2))++1/(s...

    Text Solution

    |