Class 12

Math

Calculus

Area

The area of the figure bounded by the parabola $(y−2)_{2}=x−1,$ the tangent to it at the point with the ordinate x=3, and the x-axis is

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Area of region bounded by the curve $y=416−x_{2} $ and $y=sec_{−1}[−sin_{2}x]$ (where [x] denotes the greatest ingeger function) is

The ratio in which the line $x−1=0$ divides the area bounded by the curves $2x+1=4y+1 ,y=xandy=2$ is

The area (in sq. units) of the region ${(x,y):y_{2}≥2xandx_{2}+y_{2}≤4x,x≤0,y≥0}$ is

$Two curvesC_{1}≡[f(y)]_{2/3}+[f(x)]_{1/3}=0andC_{2}≡[f(y)]_{2/3}+[f(x)]_{2/3}=12,satisfying the relation(x−y)f(x+y)−(x+y)f(x−y)=4xy(x_{2}−y_{2})$ The area bounded by $C_{1}andx+y+2=0$ is

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

Match the following lists :

The area bounded by the graph of $y=f(x),f(x)>0$ on [0,a] and x-axis is $2a_{2} +2a sina+2π cosa$ then find the value of $f(2π )$.

Find the area of the region enclosed by the curve $y=∣∣ x−x1 ∣∣ (x>0)$ and the line y=2