Home
Class 12
MATHS
Computing area with parametrically repre...

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., `x=x(t), y=(t),` then the area of the figure is evaluated by one of the three formulas :
`S=-overset(beta)underset(alpha)inty(t)x'(t)dt,`
`S=overset(beta)underset(alpha)intx(t)y'(t)dt,`
`S=(1)/(2)overset(beta)underset(alpha)int(xy'-yx')dt,`
Where `alpha and beta` are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t.
The area of the region bounded by an are of the cycloid `x=a(t-sin t), y=a(1- cos t)` and the x-axis is

A

`6pia^2`

B

`3pi a^2`

C

`4pi a^2`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|8 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|17 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|5 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

Similar Questions

Explore conceptually related problems

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta)y(t)x'(t)dt, S=int_(alpha)^(beta)x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. The area of the region bounded by an are of the cycloid x=a(t-sin t), y=a(1- cos t) and the x-axis is

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta)y(t)x'(t)dt, S=int_(alpha)^(beta)x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. The area of the loop described as x=(t)/(3)(6-t),y=(t^(2))/(8)(6-t) is

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., x=x(t), y=(t), then the area of the figure is evaluated by one of the three formulas : S=-int_(alpha)^(beta) y(t)x'(t)dt, S=int_(alpha)^(beta) x(t)y'(t)dt, S=(1)/(2)int_(alpha)^(beta)(xy'-yx')dt, Where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of the traversal of the curve corresponding to increasing t. If the curve given by parametric equation x=t-t^(3), y=1-t^(4) forms a loop for all values of t in [-1,1] then the area of the loop is

Computing area with parametrically represented boundaries If the boundary of a figure is represented by parametric equations x = x (t) , y = y(t) , then the area of the figure is evaluated by one of the three formulae S = -int_(alpha)^(beta) y(t) x'(t) dt , S = int_(alpha)^(beta) x (t) y' (t) dt S = (1)/(2) int_(alpha)^(beta) (xy'-yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of traversal of the contour . The area of ellipse enclosed by x = a cos t , y = b sint (0 le t le 2pi)

Computing area with parametrically represented boundaries If the boundary of a figure is represented by parametric equations x = x (t) , y = y(t) , then the area of the figure is evaluated by one of the three formulae S = -int_(alpha)^(beta) y(t) x'(t) dt , S = int_(alpha)^(beta) x (t) y' (t) dt S = (1)/(2) int_(alpha)^(beta) (xy'-yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of traversal of the contour . The area enclosed by the astroid ((x)/(a))^((2)/(3)) + ((y)/(a))^((2)/(3)) = 1 is

If alpha and beta are the zeros of the quadratic polynomial f(t)=t^(2)-4t+3, find the value of alpha^(4)beta^(3)+alpha^(3)beta^(4)