Home
Class 12
MATHS
Evaluate: If intcos^nxdotdx prove that I...

Evaluate: If `intcos^nxdotdx` prove that `I_n=1/n(cos^(n-1)xsinx)+((n-1)/n)I_(n-2)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • INEQUALITIES INVOLVING MEANS

    CENGAGE ENGLISH|Exercise Jee Advanced (Single|1 Videos
  • INTRODUCTION TO VECTORS

    CENGAGE ENGLISH|Exercise MATRIX-MATCH TYPE|3 Videos

Similar Questions

Explore conceptually related problems

If I_n=intxcos^nxdx,prove that: I_n=1/n cos^(n-1)x(sinx)+(n-1)/(n)I_(n-2)

If I_(n)=int cos^(n)x dx . Prove that I_(n)=(1)/(n)(cos^(n-1)x sinx)+((n-1)/(n))I_(n-2) .

If I_(m,n)= int(sinx)^(m)(cosx)^(n) dx then prove that I_(m,n) = ((sinx)^(m+1)(cosx)^(n-1))/(m+n) +(n-1)/(m+n). I_(m,n-2)

Prove that ((n + 1)/(2))^(n) gt n!

If I_(n)=int(sinx+cosx)^(n) dx, snd I_(n)=1/n(sinx+cosx)^(n-1)(sinx-cosx)+(2k)/(n) I_(n-2) then k=

Prove that: n !(n+2)=n !+(n+1)!

Prove that: n(n-1)(n-2)....(n-r+1)=(n !)/((n-r)!)

If I_n=int x^nsqrt(a^2-x^2)dx, prove that I_n=-(x^(n-1)(a^2-x^2)^(3/2))/((n+2))+((n+1))/((n+2))a^2I_(n-2)

Prove that [(n+1)//2]^n >(n !)dot

If I_(m"," n)=int cos^(m)x*cos nx dx , show that (m+n)I_(m","n)=cos^(m)x*sin nx+m I_((m-1","n-1))

CENGAGE ENGLISH-INTEGRALS-All Questions
  1. Evaluate: intsqrt((3-x)/(3+x))sin^(-1)(1/6sqrt(3-x))dx

    Text Solution

    |

  2. Evaluate: int((1-xsinx)dx)/(x(1-x^3e^(3cosx)))

    Text Solution

    |

  3. Evaluate: If intcos^nxdotdx prove that In=1/n(cos^(n-1)xsinx)+((n-1)/n...

    Text Solution

    |

  4. Evaluate: int(x^2-1)/(xsqrt((x^2+alphax+1)(x^2+betax+1)))dx

    Text Solution

    |

  5. Evaluate: int(e^(tan^(-1)x))/((1+x^2))[(sec^(-1)sqrt(1+x^2)+cos^(-1)(...

    Text Solution

    |

  6. int(sqrt(x-1))/(xsqrt(x+1))dxi se q u a lto ln|x-sqrt(x^2-1)|-tan^(-1...

    Text Solution

    |

  7. IfI=int(dx)/((2a x+x^2)^(3/2)),then I is equal to (a)-(x+a)/(sqrt(2a ...

    Text Solution

    |

  8. If f^(prime)(x)=1/(-x+sqrt(x^2+1)) and f(0)=(1+sqrt(2))/2 then f(1) ...

    Text Solution

    |

  9. inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dxi se q u a lto e^xtan(pi/4-x)...

    Text Solution

    |

  10. The value of the integral int(x^2+x)(x^(-8)+2x^(-9))^(1/(10))dx is 5/(...

    Text Solution

    |

  11. Ifint(dx)/((x+2)(x^2+1))=aln(1+x^2)+btan^(-1)x+1/5ln|x+2|+C Then (a) ...

    Text Solution

    |

  12. If int (3sinx+2cosx)/ (3cosx+2sinx) dx=a x+b ln|2sinx+3cosx|+C, then (...

    Text Solution

    |

  13. Ifint(3e^x-5e^(-x))/(4e^x+5e^(-x))dx=a x+bln(4e^x+5e^(-x))+C ,t h e n ...

    Text Solution

    |

  14. intsqrt((cosx-cos^3x)/(1-cos^3x))dx is equal to (a) -2/3sin^(-1)(cos...

    Text Solution

    |

  15. If l^(prime)(x) means logloglog x , the log being repeated r times, th...

    Text Solution

    |

  16. int(cos4x-1)/(cotx-tanx)dx is equal to (A) 1/2ln|sec2x|-1/4cos^2 2x+...

    Text Solution

    |

  17. If int(dx)/(sqrt(sin^3xcos^5x))=asqrt(cotx)+bsqrt(tan^3)x+c , then (...

    Text Solution

    |

  18. int e^(tan^(-1)x)(1+x+x^2)d(cot^(-1)x) is equal to (a) -e^(tan^(-1)x)...

    Text Solution

    |

  19. int(x^9dx)/((4x^2+1)^6) is equal to (a)1/(5x)(4+1/(x^2))^(-5)+c (b...

    Text Solution

    |

  20. int(2sinx)/(3+sin2x)dx is equal to

    Text Solution

    |