Home
Class 12
MATHS
The area bounded by the curve y =ln(x) a...

The area bounded by the curve `y =ln(x)` and the lines `y = 0, y =ln(3)` and `x = 0` is equal to

A

3 sq units

B

3 In (3) - 2sq units

C

3 In (3) + 2 sq units

D

2 sq units

Text Solution

Verified by Experts

The correct Answer is:
D
`therefore` Required area `=int_(0)^(log3)xdy=int_(0)^(log3)e^(y)dy(because "y = in x")`
`=[e^(y)]_(0)^(log3)=[e^(log3)-e^(0)]=3-1=2`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|6 Videos

  • APPLICATIONS OF DEFINITE INTEGRALS

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET Corner|6 Videos

  • APPLICATIONS OF DERIVATIVES

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise MHT CET CORNER|21 Videos

Similar Questions

Explore conceptually related problems

The area bounded by the curve y^(2) = 4x and the line 2x-3y+4=0 is

Find the area bounded by the curves y=4-x^(2) and the lines y=0 and y=3

The area bounded by the curve y= f(x) and the lines x=0, y=0 and x=t , lies in the interval

Find the area bounded by the curve y=4-x^(2) and the line y=0 and y=3 .

The area bounded by the curves y=In x,y=|ln x| and the y-axis is

The area bounded by the curves y=-x^(2)+3 " and " y=0 is

The area bounded by the curve x^(2)=4y+4 and line 3x+4y=0 is

The area bounded by the curve x=3y^2-9 and the line x=0,y=0 and y=1 is

Find the area bounded by the curve y=(4-x^2) the y-axis and the lines y=0 y=3

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DEFINITE INTEGRALS -Exercise 2
  1. What is the area bounded by the curves y=e^x ,y =e ^-x and the straig...

    Text Solution

    |

  2. The area between the curve y=2x^(4)-x^(2), the x-axis, and the ordinat...

    Text Solution

    |

  3. The area bounded by the curve y =ln(x) and the lines y = 0, y =ln(3) a...

    Text Solution

    |

  4. The area bounded between the parabolas x^2=y/4"and"x^2=9y and the s...

    Text Solution

    |

  5. The area of the figure bounded by the curves y^(2)=2x+1 and x-y-1=0 , ...

    Text Solution

    |

  6. The area of the plane region bounded by the curves x + 2y^(2)=0 and x+...

    Text Solution

    |

  7. The area enclosed between the curves y = x^(3) and y = sqrt(x) is

    Text Solution

    |

  8. The area enclosed between the parabola y = x^(2)-x+2 and the line y = ...

    Text Solution

    |

  9. The area bounded by the curves y^(2)=4a^(2)(x-1) and lines x = 1 and y...

    Text Solution

    |

  10. The area bounded by the curves y = cos x and y = sin x between the ord...

    Text Solution

    |

  11. The area of the plane region bounded by the curve x = y^(2)-2 and the ...

    Text Solution

    |

  12. The area bounded by the curve y = 2x - x^(2) and the line y = - x is

    Text Solution

    |

  13. For 0 lt= x lt= pi, the area bounded by y = x and y = x + sin x, is

    Text Solution

    |

  14. If the area above the x-axis, bounded by the curves y = 2^(kx) and x =...

    Text Solution

    |

  15. The area of the region described by A = {(x,y) : x^2 + y^2 lt= 1and y^...

    Text Solution

    |

  16. The area in the first quadrant between x^2+y^2=pi^2 and y=sinx is

    Text Solution

    |

  17. The area bounded by the curves y=sqrtx, 2y-x+3=0, X-axis and lying in ...

    Text Solution

    |

  18. The area bounded by y = |sin x|, X-axis and the line |x|=pi is

    Text Solution

    |

  19. Find the area bounded by the x-axis, part of the curve y=(1-8/(x^2)) ,...

    Text Solution

    |

  20. The area bounded by the graph of y=f(x), f(x) gt0 on [0,a] and x-axis ...

    Text Solution

    |