Class 12

Math

Calculus

Area

The area bounded by the curve $a_{2}y=x_{2}(x+a)$ and the x-axis is

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Find the area bounded by the curve $f(x)=x+sinxand$ its inverse function between the ordinates $x=0tox=2π$.

The area bounded by the curves $y=xe_{x},y=xe_{−x}$ and the line x=1 is

The area bounded between the parabolas $x_{2}=4y andx_{2}=9y$ and the straight line y=2 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

$Iff:[−1,1]→[−21 ,21 ],f(x)=1+x_{2}x ,$ then find the area bounded by $y=f_{−1}(x),x$ axis and lines $x=21 ,x=−21 .$

Match the following lists :

If the area enclosed by the curve $y=x andx=−y ,$ the circle $x_{2}+y_{2}=2$ above the x-axis is A, then the value of $π16 $A is__.