Home
Class 12
MATHS
Evaluate the following integral: int(-pi...

Evaluate the following integral: `int_(-pi//4)^(pi//4)|s in x|dx`

Text Solution

Verified by Experts

I=`int_(-pi//4)^(pi//4)|sinx|dx`
I=`int_(-pi//4)^(0)(-sinx)dx+int_0^(pi//4)(sinx)dx`
`I=(cosx)_(−π/4)^0​−(−cosx)_0^(π/4)`
​ `I=1−1/sqrt(2 )​​+1/sqrt(2) ​+1=2`
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 integrals: int_(-pi/4)^(pi/4)|sin x| dx

Evaluate the following integral: int_(-pi//4)^(pi//4)sin^2x\ dx

Evaluate the following integral: int_(-pi/4)^( pi/4)|tan x|dx

Evaluate the following integral: int_(-pi//2)^(pi//2)sin^4x\ dx

Evaluate the following integral: int_(-pi//2)^(pi//2)sin^3x\ dx

Evaluate the following integral: int_(-pi//2)^(pi//2)sin^9x\ dx

Evaluate the following integral: int_(-pi//2)^(pi//2)sin^9x\ dx

Evaluate the following integral: int_(-pi//2)^(pi//2)(2sin|x|+cos x)dx

Evaluate the following integral: int_(-pi//2)^(pi//2)(sin|x|+"cos"|x|)dx

Evaluate the following integral: int_(0)^( pi/4)e^(x)s in xdx

RD SHARMA-DEFINITE INTEGRALS-Solved Examples And Exercises
  1. Evaluate the following integral: int0^3|3x-1|dx

    Text Solution

    |

  2. Evaluate the following integral: int(-2)^2|x+1|dx

    Text Solution

    |

  3. Evaluate the following integral: int(-pi//4)^(pi//4)|s in x|dx

    Text Solution

    |

  4. Evaluate the following integral: int(-pi//2)^(pi//2)|sinx+"cosx|dx

    Text Solution

    |

  5. Evaluate the following integral: int1^4{|x-1|+|x-2|+|x-4|}dx

    Text Solution

    |

  6. Evaluate the following integral: int(-pi//2)^(pi//2)(2sin|x|+cos x)dx

    Text Solution

    |

  7. Evaluate of each of the following integral: int0^(2pi)(dx)/(e^(sinx)+1...

    Text Solution

    |

  8. Evaluate of each of the following integral: int(-pi//4)^(pi//4)(tan^2x...

    Text Solution

    |

  9. Evaluate of each of the following integral: int(-pi//3)^(pi//3)1/(1+e^...

    Text Solution

    |

  10. Evaluate of each of the following integral: int0^(pi//2)(2logcos x-log...

    Text Solution

    |

  11. Evaluate of each of the following integral: int(pi//6)^(pi//3)1/(1+sqr...

    Text Solution

    |

  12. Evaluate of each of the following integral: int(-pi//2)^(pi//2)(cos^2x...

    Text Solution

    |

  13. Evaluate of each of the following integral: inta^b(x^(1//n))/(x^(1//n)...

    Text Solution

    |

  14. Evaluate of each of the following integral: int0^a(sqrt(x))/(sqrt(x)+s...

    Text Solution

    |

  15. If f(a+b-x)=f(x),\ then prove that\ inta^b xf(x)dx=(a+b)/2inta^bf(x)d...

    Text Solution

    |

  16. Evaluate: int0^(pi//2)(sqrt(s in x))/(sqrt(s in x)+sqrt(cos x))dx

    Text Solution

    |

  17. Evaluate: int0^(pi//2)logtanx\ dx

    Text Solution

    |

  18. Evaluate: int0^(pi//4)"log"(1+"t a n x")dx

    Text Solution

    |

  19. Evaluate: int0^(pi//2)(s in x-cosx)/(1+s in xcosx)dx

    Text Solution

    |

  20. Evaluate: int0^(pi//2)(2logsinx-logsin2x)dx

    Text Solution

    |