Class 12

Math

Calculus

Area

The area of the closed figure bounded by $y=2x_{2} −2x+2$ and the tangents to it at $(1,1/2)$ and (4,2) is

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The area enclosed between $y=sin2x,y=3 sinx$ between $x=0andx=π$ is

The area enclosed by the curve $C:y=x9−x_{2} (x≥0)$ and the x-axis is___.

If the area bounded between x-axis and the graph of $y=16x−3x_{2}$ between the ordinates $x=1$ and x = a is 19 square units, then take a can take the value

Let $C_{1}andC_{2}$ be the graphs of the functions $y=x_{2}andy=2x,$ respectively, where $0≤x≤1.LetC_{3}$ be the graph of a function y=f(x), where $0≤x≤1,f(0)=0.$ For a point P on $C_{1},$ let the lines through P, parallel to the axes, meet $C_{2}andC_{3}$ at Q and R, respectively (see figure). If for every position of $P(onC_{1}),$ the areas of the shaded regions OPQ and ORP are equal, determine the function f(x).

The area of the closed figure bounded by $x=−1x=2,$ and $y={−x_{2}+2,2x−1, x≤1x>1 $ and the abscissa axis is

Consider two curves $C_{1}:y=x1 andC_{2}:y=$ In x on the xy plane. Let $D_{1}$ denotes the region surrounded by $C_{1},C_{2},$ and the line x=1 and $D_{2}$ denotes the region surrounded by $C_{1},C_{2}and the line x=a. IfD_{1}=D_{2},$ then the sum of logarithm of possible values of a is ___.

Area bounded by the min. ${∣x∣,∣y∣}=1$ and the max. ${∣x∣,∣y∣}=2$ is

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