Class 12

Math

Calculus

Area

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

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Find the area bounded by the curve $x=⎩⎨⎧ −2−y,y_{3},2−y, y<−1−1≤y≤1y>1 $ and x=0 is

Consider the two curves $C_{1}:y=1+cosxandC_{2}:y=1+cos(x−α)forα∈(0,2π ),wherex∈[0,π].$ Also the area of the figure bounded by the curves $C_{1},C_{2},andx=0$ is same as that of the figure bounded by $C_{2},y=1,andx=π$. The value of $α$ is

The area bounded by the loop of the curve $4y_{2}=x_{2}(4−x_{2})$ is

The area bounded by the curve $y=sin_{2}x−2sinx$ and the x-axis, where $x∈[0,2π]$, is

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

Find the area of the region enclosed by $y=−5x−x_{2}andy=x$ on interval $[−1,5]$

Area of region bounded by the curve $y=4+x_{2}4−x_{2} ,25y_{2}=9xandy=53 ∣x∣−56 $ which contains (1, 0) point in its interior is

The area bounded by the graph of $y=f(x),f(x)>0$ on [0,a] and x-axis is $2a_{2} +2a sina+2π cosa$ then find the value of $f(2π )$.