Home
Class 12
MATHS
For 0 lt= x lt= pi, the area bounded by ...

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

A

2

B

4

C

`2pi`

D

`4pi`

Text Solution

Verified by Experts

The correct Answer is:
A
Given, curves y = x and y = x + sin x intersect at (0, 0) and `(pi, pi)`.
`therefore` Required area, `A=int_(0)^(pi)(x+sinx)dx-int_(0)^(pi)xdx`
`=int_(0)^(pi)sinxdx=[-cosx]_(0)^(pi)`
`=-cospi+cos0=-(-1)+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

For 0<=x<=pi, the area bounded by y=x and y=x+sin x, is

Find the area bounded by y = sin x and axis of x in (0 , pi)

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

The area bounded by y=x|sin x| and x -axis between x=0,x=2 pi is

Find the area bounded by y=| sin x -(1)/(2)| and y= 1" for "x in [0,pi]

The area bounded by y=tan x,y=cot x,x axis in 0<=x<=(pi)/(2) is

Find the area bounded by y=sin^(-1)(sin x) and x=axis for x in[0,100 pi]

Area bounded by y=[sin x+cos x] and the lines x=0,x=pi is

Find the area bounded by y=max{0,lnx} and y lt2^x where 1/2 ltx lt1

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-APPLICATIONS OF DEFINITE INTEGRALS -Exercise 2
  1. The area of the plane region bounded by the curve x = y^(2)-2 and the ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  11. The line x = (pi)/(4) divides the area of the region bounded by y = si...

    Text Solution

    |

  12. The area bounded by the curve y=x|x|, x-axis and the ordinates x=1,x=-...

    Text Solution

    |

  13. The area (in sq units) of the region bounded by the curves y = e^(x), ...

    Text Solution

    |

  14. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

    Text Solution

    |

  15. The larger of the area bounded by y = cosx, y = x + 1 and y = 0 is

    Text Solution

    |

  16. The parabola y^2 = 2x divides the circle x^2 + y^2 = 8 in two parts. T...

    Text Solution

    |

  17. The figure shows a DeltaAOB and the parabola y = x^(2). The ratio of t...

    Text Solution

    |

  18. The area bounded by y = sin^(-1)x,x=(1)/(sqrt(2)) and X-axis is

    Text Solution

    |

  19. Find the area of the region bounded by the ellipse (x^(2))/(9)+(y^(2))...

    Text Solution

    |

  20. The area bounded by the curves y^(2)=4a(x+a) and y^(2)=4b(b-x), where ...

    Text Solution

    |