Class 12

Math

Calculus

Area

The area enclosed between the curve $y_{2}(2a−x)=x_{3}$ and the line x=2 above the x-axis is

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If the area bounded by the curve $f(x)=x_{1/3}(x−1)$ and the x-axis is A, then the value of 28A is__.

Find the area of the region enclosed by the curves y= x log x and $y=2x−2x_{2}$.

The area bounded by $y=3−∣3−x∣andy=∣x+1∣6 $ is

Find the area of the region bounded by the curves $y=x_{2},y=∣∣ 2−x_{2}∣∣ ,andy=2,$ which lies to the right of the line x=1.

Let $f:[0,∞)→R$ be a continuous function such that $f(x)=1−2x+0∫ x e_{x−t}f(t)dtfor allx∈[0,∞).$ Then, which of the following statements(s) is (are)) TRUE?

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

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