Home
Class 12
MATHS
Evaluate the following integral: int0^3|...

Evaluate the following integral: `int_0^3|3x-1|dx`

Text Solution

Verified by Experts

I=`int_0^3|3x-1|dx`
I=`int_0^(1/3)(1-3x)dx+int_(1/2)^(3)(3x-1)dx`
=`[x-3/2x^2]_0^(1/3)+[3/2x^2-x]_(1/3)^3`
=`(1/3-1/6)+(40/3-8/3)`
=`65/6`
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_0^4|x-1|dx

Evaluate the following integral: int_(-3)^3|x+1|dx

Evaluate the following integral: int_1^2|x-3|dx

Evaluate the following integral: int_(0)^(1)|2x-1|dx

Evaluate the following integral: int_0^pisin^3x(1+2cos)(1+cos x)^2dx

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

Evaluate the following integral: int_(-1)^2|2x+3|dx

Evaluate the following integrals: inte^(3x)((3x-1)/(9x^(2)))dx

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

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

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

    Text Solution

    |

  2. Evaluate the following integral: int(-1)^2|2x+3|dx

    Text Solution

    |

  3. Evaluate the following integral: int0^3|3x-1|dx

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |