Class 12

Math

Calculus

Area

The area of the region ${(x,y):x_{2}+y_{2}≤5,∣∣x∣−∣y∣∣≥1$ is

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

A farmer $F_{1}$ has a land in the shape of a triangle with vertices at $P(0,0),Q(1,1)andR(2,0).$ From this land, a neighboring farmer $F_{2}$ takes away the region which lies between the side PQ and curve of the from $y=x_{n}(n>1).$ If the area of the region taken away by the farmer $F_{2}$ is exactly $30%$ of the area of $ΔPQR$, then the value of n 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 : $S=−α∫ β y(t)x_{′}(t)dt,$ $S=α∫ β x(t)y_{′}(t)dt,$ $S=21 α∫ β (xy_{′}−yx_{′})dt,$ Where $αandβ$ 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 $t∈[−1,1]$ then the area of the loop is

Computing area with parametrically represented boundaries : If the boundary of a figure is represented by parametric equation, i.e., $x=x(t),y=(t),$ then the area of the figure is evaluated by one of the three formulas : $S=−α∫ β y(t)x_{′}(t)dt,$ $S=α∫ β x(t)y_{′}(t)dt,$ $S=21 α∫ β (xy_{′}−yx_{′})dt,$ Where $αandβ$ 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 $x=3t (6−t),y=8t_{2} (6−t)$ is

If the line $x=α$ divides the area of region $R={(x,y)∈R_{2}:x_{3}≤y≤x,0≤x≤1}$ into two equal parts, then

The parabolas $y_{2}=4xandx_{2}=4y$ divide the square region bounded by the lines x=4, y=4 and the coordinate axes. If $S_{1},S_{2},S_{3}$ are the areas of these parts numbered from top to bottom, respectively, then

Let $O(0,0),A(2,0),andB(1,3 1 $ be the vertices of a triangle. Let R be the region consisting of all theose points P inside $ΔOAB$ which satisfy $d(P,OA)≤min[d(P,AB)],$ where d denotes the distance from the point to the corresponding line. Sketch the region R and find its area.

Let S is the region of points which satisfies $y_{2}<16x,x<4andx_{2}−7x+12xy(x_{2}−3x+2) >0$. Its area is