Class 12

Math

Calculus

Area

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

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The parabolas $y_{2}=4xandx_{2}=4y$ divide the square region bounded by the lines x=4, y=4 and the coordinate axes. If $S_{1},S_{2},S_{3}$ are the areas of these parts numbered from top to bottom, respectively, then

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___.

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

Find the area of curve enclosed by $∣x+y∣+∣x−y∣≤4,∣x∣≤1,y≥x_{2}−2x+1 $.

Match the following lists :

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?

The area in the first quadrant between $x_{2}+y_{2}=π_{2}$ and $y=sinx$ is

The area enclosed between the curve $y=sin_{2}xandy=cos_{2}x$ in the interval $0≤x≤π$ is