Class 12

Math

Calculus

Area

Find the area of the region bounded by the curves $y=x+2 andy=x+11 $ between the lines x=0 and x=2.

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The area bounded by the curves $y=x(x−3)_{2}andy=x$ is ___ (in sq. units).

Consider the function defined implicity by the equation $y_{2}−2ye_{sin_{−1}x}+x_{2}−1+[x]+e_{2sin_{−1}x}=0(where [x] denotes the greatest integer function).$ The area of the region of curve and line $x=0andx=21 $ is

Find the area bounded by the curve $x=⎩⎨⎧ −2−y,y_{3},2−y, y<−1−1≤y≤1y>1 $ and x=0 is

Area bounded by the relation $[2x]+[y]=5,x,y>0$ is__ (where [.] represents greatest integer funciton).

Area enclosed by the curve $y=f(x)$ defined parametrically as $x=1+t_{2}1−t_{2} ,y=1+t_{2}2t $ is equal to

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

Find the area bounded by the curve $x_{2}=y,x_{2}=−y,andy_{2}=4x−3.$

Find a continuous function f, where $(x_{4}−4x_{2})≤f(x)≤(2x_{2}−x_{3})$ such that the area bounded by $y=f(x),y=x_{4}−4x_{2},$ the y-axis, and the line $x=t,where(0≤t≤2)$ is k times the area bounded by $y=f(x),y=2x_{2}−x_{3},$ y-axis, and line $x=t(where0≤t≤2).$