Class 12

Math

Calculus

Area

The area bounded by the curve $y_{2}(2−x)=x_{3}andx=2$ is

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Let $A_{r}$ be the area of the region bounded between the curves $y_{2}=(e_{−kr})x(wherek>0,r∈N)and the liney=mx(wherem=0)$, k and m are some constants $n→∞lim i=1Σ n A_{i}=48(e_{2k}−1)1 $ then the value of m is

Area of the region bounded by the curve $y=tanx$ and lines y = 0 and x = 1 is

The area enclosed by the curves $x=asin_{3}tandy=acos_{2}t$ is equal to

The area (in square units) bounded by the curves $y=x ,2y−x+3=0,$ x-axis, and lying in the first quadrant is

The area bounded by the curve $y=xe_{−x},y=0andx=c,$ where c is the x-coordinate to the curve's inflection point, is

$Givenf(x)=0∫ x e_{t}(g_{e}sect−sec_{2}t)dt,g(x)=−2e_{x}tanx,$ then the area bounded by the curves $y=f(x)andy=g(x)$ between the ordinates $x=0andx=3π ,$ is (in sq. units)

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

Find the area of the region bounded by the x-axis and the curves defined by $y=tanx(where−3π ≤x≤3π )andy=cotx(where6π ≤x≤23π ).$