Class 12

Math

Calculus

Area

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

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If the area bounded by the curve $y=x_{2}+1$ and the tangents to it drawn from the origin is A, then the value of 3A is __.

Let f(x) be a non-negative continuous function such that the area bounded by the curve y=f(x), the x-axis, and the ordinates $x=4π andx=β>4π isβsinβ+4π cosβ+2 β.$ Then $f_{′}(2π )$ is

If the area bounded by the x-axis, the curve $y=f(x),(f(x)>0)and the linesx=1,x=bis equal tob_{2}+1 −2 for allb>1,$ then find f(x).

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

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 region bounded by an are of the cycloid $x=a(t−sint),y=a(1−cost)$ and the x-axis is

The area enclosed by $f(x)=12+ax±x_{2}$ coordinates axes and the ordinates at $x=3(f(3)>0)$ is 45 sq. units. If m and n are the x-axis intercepts of the graph of y=f(x), then the value of (m+n+a) si ___.

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__.

Area enclosed between the curves $∣y∣=1−x_{2}andx_{2}+y_{2}=1$ is