Home
Class 12
MATHS
The area in the first quadrant between x...

The area in the first quadrant between `x^2+y^2=pi^2` and `y=sinx` is (a) `((pi^(3)-8))/(4)` (b) `(pi^(3))/(4)` (c) `((pi^(3)-16))/(4)` (d) `((pi^(3)-8))/(2)`

A

`((pi^(3)-8))/(4)`

B

`(pi^(3))/(4)`

C

`((pi^(3)-16))/(4)`

D

`((pi^(3)-8))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Graph of the function is as shown in the following figure:

From the figure bounded area A
`="(Area of quarter of circle)"-("Area bounded by y = sin x and x-axis between x = 0 and x "=pi//2)`
`=(pi(pi)^(2))/(4)-2`
`=((pi^(3)-8))/(4)`
Promotional Banner

Topper's Solved these Questions

  • AREA

    CENGAGE PUBLICATION|Exercise Multiple Correct Answer Type|3 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Comprehension Type|2 Videos

  • AREA

    CENGAGE PUBLICATION|Exercise Archives|10 Videos

  • APPLICATIONS OF DERIVATIVES

    CENGAGE PUBLICATION|Exercise Subjective Type|2 Videos

  • BINOMIAL THEOREM

    CENGAGE PUBLICATION|Exercise Comprehension|11 Videos

Similar Questions

Explore conceptually related problems

Area enclosed between the curves |y|=1-x^2 and x^2+y^2=1 is (a) (3pi-8)/3 (b) (pi-8)/3 (c) (2pi-8)/3 (d) None of these

int_0^pi(xtanx)/(secx+cosx)dx is (pi^2)/4 (b) (pi^2)/2 (c) (3pi^2)/2 (d) (pi^2)/3

The area enclosed by the curve y=sqrt(4-x^2),ygeqsqrt(2)sin((xpi)/(2sqrt(2))) , and the x-axis is divided by the y-axis in the ratio. (a) (pi^2-8)/(pi^2+8) (b) (pi^2-4)/(pi^2+4) (c) (pi-4)/(pi-4) (d) (2pi^2)/(2pi+pi^2-8)

2 sin ^(2) "" (3pi)/(4) + 2 cos ^(2) "" (pi)/( 4) + 2 sec ^(2) "" (pi)/(3) =10

The angle between the tangents to the curve y=x^2-5x+6 at the point (2, 0) and (3, 0) is (a) pi/2 (b) pi/3 (c) pi (d) pi/4

The angles at which the circles (x-1)^2+y^2=10 and x^2+(y-2)^2=5 intersect is pi/6 (b) pi/4 (c) pi/3 (d) pi/2

2tan^(-1)(-2) is equal to (a) -cos^(-1)((-3)/5) (b) -pi+cos^(-1)3/5 (c) -pi/2+tan^(-1)(-3/4) (d) -pi+cot^(-1)(-3/4)

Let I=int_((pi)/(4))^((pi)/(3))(sinx)/(x)dx . Then

In which of the following intervals the inequality, sinx < cos x < tanx < cot x can hold good ? (a) ((7pi)/4,2pi) (b) ((3pi)/4,pi) (c) ((5pi)/4,(3pi)/2) (d) (0,(pi)/4)

Evalute : "sin"^(2)(pi)/(4) + "cos"^(2) (3pi)/(4)+"cos"^(2)(5pi)/(4)+"sin"^(2)(7pi)/(4).

CENGAGE PUBLICATION-AREA-Single Correct Answer Type
  1. The area bounded by the curve y=|cos^(-1)(sinx)|-|sin^(-1)(cosx)| and ...

    Text Solution

    |

  2. If (a,0), agt 0, is the point where the curve y=sin 2x-sqrt3 sin x cut...

    Text Solution

    |

  3. The area in the first quadrant between x^2+y^2=pi^2 and y=sinx is (a) ...

    Text Solution

    |

  4. The area bounded by the curves y=cos^(-1)x,y =sin^(-1) x and y=-pix^(3...

    Text Solution

    |

  5. The area bounded by the curve y=sin^(2)x-2 sin x and the x-axis, wher...

    Text Solution

    |

  6. Consider the functions f(x) and g(x), both defined from R rarrR and ar...

    Text Solution

    |

  7. Let a function f(x) be defined in [-2, 2] as f(x) = {{:({x}",",, -2 ...

    Text Solution

    |

  8. The area bounded by y=x^(2)+2 and y=2|x|-cospi x is equal to

    Text Solution

    |

  9. Area bounded by f(x)=(x^(2)-1)/(x^(2)+1) and the line y = 1 is

    Text Solution

    |

  10. The area bounded by the curve y=xe^(-x);xy=0and x=c where c is the x-c...

    Text Solution

    |

  11. Area of region bounded by the curve y=(16-x^(2))/(4) and y=sec^(-1)[-s...

    Text Solution

    |

  12. Suppose y=f(x) and y=g(x) are two continuous functiond whose graphs in...

    Text Solution

    |

  13. The ratio of the areas of two regions of the curve C(1)-=4x^(2)+pi^(2)...

    Text Solution

    |

  14. The area bounded by the curves xsqrt3+y=2log(e)(x-ysqrt3)-2log(e)2, ...

    Text Solution

    |

  15. Area of region bounded by the curve y=(4-x^(2))/(4+x^(2)), 25y^(2)=9x ...

    Text Solution

    |

  16. Area bounded by the min. {|x|,|y|}=1 and the max. {|x|,|y|}=2 is

    Text Solution

    |

  17. Consider f(x)={{:(cosx,0lexlt(pi)/(2)),(((pi)/(2)-x)^(2),(pi)/(2)lexlt...

    Text Solution

    |

  18. The area made by curve f(x)=[x]+sqrt(x-[x]) and x-axis when 0le xle n ...

    Text Solution

    |

  19. Consider the regions A={(x,y)|x^(2)+y^(2)le100} and B=|(x,y)|sin(x+y)g...

    Text Solution

    |

  20. Let R be the region containing the point (x, y) on the X-Y plane, sati...

    Text Solution

    |