Home
Class 12
MATHS
The primitive of the function f(x) =xabs...

The primitive of the function f(x) `=xabs(cosx)`, when `x in (pi/2, pi)` is

A

x sin x + cos x + c

B

x cos x + sin x + c

C

-x sin x - cos x + c

D

x cosx - sin x + c

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRAL

    PATHFINDER|Exercise QUESTION BANK|39 Videos

  • MATRICES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

Find the point at which the slope of the tangent of the function f(x)=e^xcosx attains maxima, when x in [-pi,pi]dot

Verify the truth of Rolle's theorem for the functions: f(x)=cosx " in " [-(pi)/(2), (pi)/(2)]

Examine the differentiability of the function f(x)=|sinx-cosx| at x=(pi)/(4) .

Examine whether Rolle's theorem is applicable to the function f(x) = cot x in -pi/2le x le pi/2

Examine the differentiability of the function f(x)=|cosx| at x=(pi)/(2) .

If [2sinx]+[cosx]=-3 then the range of the function f(x)=sinx+sqrt3cosx in [0, 2pi] is, (where [.] denotes the greatest integer function)

Find the period of the function f(x) = sin((pi x)/3) + cos ((pi x)/2) .

The greatest value of the function f(x)=(sin2x)/(sin(x+pi/4)) on the interval (0,pi/2) \ i s

Verify Rolle's theorem for the function f(x) = sin x + cosx in the interval ole x le pi//2

Verify Rolle's theorem for the functions f(x)=e^(-x)(sinx-cosx)" in " (pi)/(4) le x le (5pi)/(4)

PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
  1. Integral of sqrt(1 + 2cot x (cot x + cosec x)) w.r.t.x, is

    Text Solution

    |

  2. int (e^(2001x) + e^(1999x))/(e^x + e^-x) dx is

    Text Solution

    |

  3. The primitive of the function f(x) =xabs(cosx), when x in (pi/2, pi) i...

    Text Solution

    |

  4. If int tan^4 x dx = a tan^3 x + b tan x + phi(x) then

    Text Solution

    |

  5. If int sinx/sin(x-alpha) dx = Ax + B log sin(x - alpha) + c

    Text Solution

    |

  6. If int (4e^x + 6e^-x)/(9e^x - 4e^-x) dx = Ax + B loge(9e^(2x) - 4) + c...

    Text Solution

    |

  7. If int x log(1 + x^2) dx = phi(x) log(1 + x^2) + psi(x) + c then

    Text Solution

    |

  8. int dx/((x+1)(x-2)) = A log (x + 1) + B log (x - 2) + c where

    Text Solution

    |

  9. If int (xe^x)/(sqrt(1 + e^x)) dx = f(x) sqrt(1 + e^x) - 2 In g(x) + c...

    Text Solution

    |

  10. If I = int (sin x + sin^3 x)/(cos 2x) dx = A cos x + B log abs(f(x)) +...

    Text Solution

    |

  11. If int (xe^x)/(sqrt(1 + e^x)) dx = f(x) sqrt(1 + e^x) - 2 In g(x) + c...

    Text Solution

    |

  12. The value of int0^x (t - abst)^2/(1 + t^2) dt is equal to

    Text Solution

    |

  13. int dx/((x+1)(x+2)) = A log (x + 1) + B log (x +2) + c where

    Text Solution

    |

  14. Let f(x) = 3/( 3x^2 + 9) and g(x)=x^2/( 3x^2 + 9) int (f(x) + g(x)) ...

    Text Solution

    |

  15. Let f(x) = 3/( 3x^2 - 9) and g(x)=x^2/( 3x^2 - 9) int (g(x) - f(x)) ...

    Text Solution

    |

  16. If i(m - 2 , n + 2) = int sin^(m - 2)x cos^(n+2)x dx and I(m,n) = - (s...

    Text Solution

    |

  17. If In = int x sin^n x dx and In = -(x sin^(n-1)x cos x)/n + (sin^n x)/...

    Text Solution

    |

  18. Match List - I with List-II Let the functions defined in List - I ha...

    Text Solution

    |

  19. Match List - I with List-II Let the functions defined in List - I ha...

    Text Solution

    |

  20. If int xdx/sqrt(7x - 10 - x^2)^3 = (lambda(7x - 20))/sqrt(7x - 10 - x^...

    Text Solution

    |