Home
Class 12
MATHS
Evaluate the following integral: int0^1(...

Evaluate the following integral: `int_0^1(cos^(-1)x)^2dx`

Text Solution

Verified by Experts

Given,I= `int_0^1(cos^(-1)x)^2dx`
Let` cos^(−1)x=y`
⇒dx=−sinydy
`I=int_0^1 ​−y^2sin(y)dy`
`I=[y^2cosy-2ysin(y)-cosy]_0^1`
=`cos(1)−2sin(1)−cos1+2.`
=`2−2sin(1)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY

    RD SHARMA|Exercise Solved Examples And Exercises|277 Videos

  • DERIVATIVES AS A RATE MEASURER

    RD SHARMA|Exercise Solved Examples And Exercises|149 Videos

Similar Questions

Explore conceptually related problems

Evaluate the following integral: int_0^1log(1/x-1)dx

Evaluate the following integral: int_0^1tan^(-1)x\ dx

Evaluate the following integral: int_(0)^(1)cos^(-1)((1-x^(2))/(1+x^(2)))dx

Evaluate the following integral: int_0^(1//2)(xsin^(-1)x)/(sqrt(1-x^2))dx

Evaluate the following integral: int_0^1(sqrt(tan^(-1)x))/(1+x^2)dx

Evaluate the following integral: int_0^1(tan^(-1)x)/(1+x^2)dx

Evaluate the following integral: int_0^4|x-1|dx

Evaluate the following integrals: int cos^(-1)(sin x)dx

Evaluate the following integral: int_0^1(1-x)/(1+x)dx

Evaluate the following integral: int_0^pilog(1-cos x)dx

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int0^(pi//2)(sin x cos x)/(cos^2x+3co...

    Text Solution

    |

  2. Evaluate the following integral: int0^(1//2)1/((1+x^2)sqrt(1-x^2))dx

    Text Solution

    |

  3. Evaluate the following integral: int0^1(cos^(-1)x)^2dx

    Text Solution

    |

  4. Evaluate the following integral: int(pi//3)^(pi//2)(sqrt(1+cosx))/((1-...

    Text Solution

    |

  5. Evaluate the following integral: int(-a)^asqrt((a+x)/(a-x))dx

    Text Solution

    |

  6. Evaluate the following integral: int(1//3)^1((x-x^3)^(1//3))/(x^4)dx

    Text Solution

    |

  7. Evaluate the following integral: int0^(pi//2)sqrt(cos x-cos^3x)"\ "(se...

    Text Solution

    |

  8. Evaluate the following integral: int0^9f(x)dx ,\ w h e r e\ f(x){sinx ...

    Text Solution

    |

  9. Evaluate the following integral: int2^4f(x)dx ,\ w h e r e\ f(x)={7x+3...

    Text Solution

    |

  10. Evaluate the following integral: int(-4)^4|x+2|dx

    Text Solution

    |

  11. Evaluate the following integral: int(-1)^1|x+1|dx

    Text Solution

    |

  12. Evaluate the following integral: int(-6)^6|x+2|dx

    Text Solution

    |

  13. Evaluate the following integral: int1^2|x-3|dx

    Text Solution

    |

  14. Evaluate the following integral: int1^(2pi)|s in x|dx

    Text Solution

    |

  15. Evaluate the following integral: int2^8|x-5|dx

    Text Solution

    |

  16. Evaluate the following integral: int0^4|x-1|dx

    Text Solution

    |

  17. Evaluate the following integral: int0^4(|x|+|x-2|+|x-4|)dx\

    Text Solution

    |

  18. Evaluate the following integral: int(-2)^2x e^(|x|)dx

    Text Solution

    |

  19. Evaluate the following integral: int(-pi//2)^pisin^(-1)(sin x)dx

    Text Solution

    |

  20. Evaluate the following integral: int(-3)^3|x+1|dx

    Text Solution

    |