Home
Class 12
MATHS
The anti-derivative of a function of the...

The anti-derivative of a function of the form `(3x − 1)f(x)`, `(x ne frac{1}{3})`, is given by `3x^4 -frac{13}{3} x^3 + frac{3}{2} x^2 + C`, where C is the constant of integration.
Find the value of f(6). Show your steps.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • QUESTION BANK 2021

    CBSE MODEL PAPER|Exercise QUESTIONS|9 Videos

Similar Questions

Explore conceptually related problems

Find the derivative at x=2 of the function f(x)=3x

If intf(x)dx=3[f(x)]^(2)+c (where c is the constant of integration) and f(1)=(1)/(6) , then f(6pi) is equal to

If x + 3frac{1}{2} = 5 , then x = ________

If the integral I=inte^(x^(2))x^(3)dx=e^(x^(2))f(x)+c , where c is the constant of integration and f(1)=0 , then the value of f(2) is equal to

If the integral int(lnx)/(x^(3))dx=(f(x))/(4x^(2))+C , where f(e )=-3 and C is the constant of integration, then the value of f(e^(2)) is equal to

Add the following: 3frac{1}{13} + 1frac{4}{13} + 2frac{3}{13}

If the integral I=int(x^(5))/(sqrt(1+x^(3)))dx =Ksqrt(x^(3)+1)(x^(3)-2)+C , (where, C is the constant of integration), then the value of 9K is equal to

Let int(x^(2)-1)/(x^(3)sqrt(3x^(4)+2x^(2)-1))dx=f(x)+c where f(1)=-1 and c is the constant of integration.

Find the anti derivative F of f defined by f(x)=4x^(3)-6 where F(0)=3

If int e^(x)((3-x^(2))/(1-2x+x^(2)))dx=e^(x)f(x)+c , (where c is constant of integration) then f(x) is equal to

CBSE MODEL PAPER-Additional Practice Questions-Question
  1. Check whether the following statement is true or false. If u = e^(si...

    Text Solution

    |

  2. If frac{x^n}{y^n}=(xy)^(m-n), (y ne 0), find frac{dy}{dx}. Show your w...

    Text Solution

    |

  3. The anti-derivative of a function of the form (3x − 1)f(x), (x ne frac...

    Text Solution

    |

  4. Evaluate the following definite integral and show your work. intfrac...

    Text Solution

    |

  5. Find the particular solution when x = y = 0 for the following differen...

    Text Solution

    |

  6. Find the general solution of the following differential equation. (x...

    Text Solution

    |

  7. Frame the below optimisation problem as a linear programming problem a...

    Text Solution

    |

  8. Nikhil has a bag of marbles that contains exactly 8 green marbles and ...

    Text Solution

    |

  9. In a recreational event at a school, there were 8 students, 6 parents,...

    Text Solution

    |

  10. Sravan is a nutritionist. He wants to create a mixture of orange juice...

    Text Solution

    |

  11. Shown below is an ellipse whose equation is frac{x^2}{81} + frac{y^2}{...

    Text Solution

    |

  12. In elastic city model, a metro track and a road above it are straight ...

    Text Solution

    |

  13. Anuj and Tara are flying kites from their rooftops. Anuj's kite's stri...

    Text Solution

    |

  14. Integrate the given function and show your steps. int x^7 sin (2x^4)...

    Text Solution

    |

  15. Evaluate the integral and show your steps. int frac{1}{8-x^3} dx

    Text Solution

    |

  16. Answer the questions based on the given information. Port Blair, the...

    Text Solution

    |

  17. Port Blair, the capital city of Andaman and Nicobar Islands is directl...

    Text Solution

    |

  18. Answer the questions based on the given information A medicinal drug...

    Text Solution

    |

  19. The amount of the drug in the bloodstream at which the action of the d...

    Text Solution

    |

  20. Answer the questions based on the given information A school conduct...

    Text Solution

    |