Class 12

Math

Calculus

Area

The area of the loop of the curve $ay_{2}=x_{2}(a−x)$ is

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Area of the region ${(x,y)∈R_{2}:y≥∣x+3∣ ,5y≤x+9≤15}$ is equal to

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 S be the area bounded by the curve $y=sinx(0≤x≤π)$ and the x-axis and T be the area bounded by the curves $y=sinx(0≤x≤2π ),y=acosx(0≤x≤2π ),$ and the x-axis $(wherea∈R_{+})$. The value of (3a) such that $S:T=1:31 $ is___.

Suppose $y=f(x)andy=g(x)$ are two functions whose graphs intersect at the three point (0, 4), (2,2) and (4, 0) with f(x) gt g(x) for 0 lt x lt 2 and f(x) lt g(x) for 2 lt x lt 4. If $∫_{0}[f(x)−g(x)]dx=10and∫_{2}[g(x)−f(x)]dx=5$, the area between two curves for 0 lt x lt 2, is

Let f(x) be a continuous function fiven by $f(x)={2x,x_{2}+ax+b, ∣x∣≤1∣x∣>1 ,then$ If f(x) is continuous for all real x then the value of $a_{2}+b_{2}$ is

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

The area enclosed by $y=x_{2}+cosxand its normal atx=2π $ in the first quadrant is

The area enclosed between the curves $y=g_{e}(x+e),x=g_{e}(y1 )$, and the x-axis is