Home
Class 12
MATHS
What is the aera under the curve y = ...

What is the aera under the curve ` y = |x| + |x-1|` between `x = 0` and `x = 1` ?

A

`1/2`

B

`1`

C

`3/2`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
B
`|x|` for `x ge 0`
`= x` and `|x - 1|` for `x le 1`
`= - (x-1)`,
so, `int_(0)^(1) (|x| + |x-|1|) = "required area"`
`a = int_(0)^(1) x dx - int_(0)^(1) (x-1)dx`
`= [(x^(2))/(2)]_(0)^(1) - [(x^(2))/(2) - x]_(0)^(1) = 1/2- (1/2 - 1) = 1 sq`. units
Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    NDA PREVIOUS YEARS|Exercise DIRECTIONS|60 Videos

  • CONICS - PARABOLA, ELLIPSE & HYPERBOLA

    NDA PREVIOUS YEARS|Exercise MATH|62 Videos

  • DERIVATIVES

    NDA PREVIOUS YEARS|Exercise MCQs|94 Videos

Similar Questions

Explore conceptually related problems

What is the area under the curve y=|x|+|x-1| between x=0 and x=1?

Find the area under the curve y =2 sqrtx between the ordinates y =0 and x =1.

Calculate the area under the curve y=2sqrtx included between the lines x = 0 and x = 1.

Calculate the area under the curve y=2sqrtx included between the lines x = 0 and x = 1.

Sketch the graph of y=|x+3| and evaluate the area under the curve y=|x+3| above x- axis and between x=6 to x=0

Compare the areas under the curves y=cos ^2 x and y= sin ^2 x between x=0 and x=pi

If A is the area lying between the curve y=sin x and x-axis between x=0 and x=pi//2 . Area of the region between the curve y=sin 2x and x -axis in the same interval is given by

Draw a rough sketch of the curve y=sqrtx-1) in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.

Draw a rough sketch of the curve y=sqrtx-1) in the interval [1, 5]. Find the area under the curve and between the lines x = 1 and x = 5.

Area under the curve y=sqrt(3x+4) between x=0 and x=4 is

NDA PREVIOUS YEARS-DEFINITE INTEGRATION & ITS APPLICATION-DIRECTIONS
  1. What is the aera under the curve y = |x| + |x-1| between x = 0 and...

    Text Solution

    |

  2. I(1) = int(pi/6)^(pi/3) (dx)/(1+sqrt(tanx)) and I(2) = (sqrt(sinx)dx)/...

    Text Solution

    |

  3. I(1) = int(pi/6)^(pi/3) (dx)/(1+sqrt(tanx)) and I(2) = (sqrt(sinx)dx)/...

    Text Solution

    |

  4. What is int(-pi/2)^(pi/2) x sinx dx equal to ?

    Text Solution

    |

  5. What is int(0)^(pi/2) ln(tanx) dx equal to ?

    Text Solution

    |

  6. Find the area of the parabola y^2=4a xbounded by its latus rectum.

    Text Solution

    |

  7. Consider I = int(0)^(pi) (xdx)/(1+sinx) What is I equal to ?

    Text Solution

    |

  8. Consider I = int(0)^(pi) (xdx)/(1+sinx) What is int(0)^(pi)((pi-x)...

    Text Solution

    |

  9. Consider I = int(0)^(pi) (xdx)/(1+sinx) What is int(0)^(pi) (dx)/(1...

    Text Solution

    |

  10. Consider is int(0)^(pi//2) ln (sinx)dx equal to ? What is int(0)^(pi...

    Text Solution

    |

  11. Consider is int(0)^(pi//2) ln (sinx)dx equal to ? What is int(0)^(pi...

    Text Solution

    |

  12. What is int(0)^(pi//2) (dx)/(a^(2) cos^(2) x+ b^(2) sin^(2) x) equal t...

    Text Solution

    |

  13. The area of a triangle, whose verticles are (3,4) , (5,2) and the p...

    Text Solution

    |

  14. प्रथम चतुर्थांश में वृत्त x^(2)+y^(2)=4, रेखा x=sqrt(3)y एवं x-अक्ष द...

    Text Solution

    |

  15. Find the area of the region in the first quadrant enclosed by x-a xi s...

    Text Solution

    |

  16. Consider the curves y= sin x and y = cos x. What is the area of the re...

    Text Solution

    |

  17. Consider the curves y = sin x and y = cos x . What is the area of ...

    Text Solution

    |

  18. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

    Text Solution

    |

  19. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

    Text Solution

    |

  20. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

    Text Solution

    |

  21. Consider the integral I(m) = int(0)^(pi) (sin2mx)/(sinx ) dx, where ...

    Text Solution

    |