Class 12

Math

Calculus

Area

The area of the region containing the points (x,y) satisfy- ing $4≤x_{2}+y_{2}≤2(∣x∣+∣y∣)$ is

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Consider the area $S_{0},S_{1},S_{2}….$ bounded by the x-axis and half-waves of the curve $y=e_{−x}sinx,wherex≥0.$ The sequence $S_{0},S_{1},S_{2},…,$ forms a G.P. with common ratio

Consider curves $S_{1}:∣x∣ +∣y∣ =a ,S_{2}:x_{2}+y_{2}=a_{2}andS_{3}:∣x∣+∣y∣=a.Ifαis area bounded byS_{1}andS_{2},βis area bounded byS_{1}andS_{3}andγ$ is the area bounded by $S_{2}andS_{3},$ then

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 S is the region of points which satisfies $y_{2}<16x,x<4andx_{2}−7x+12xy(x_{2}−3x+2) >0$. Its area is

Find the area of the region bounded by the x-axis and the curves defined by $y=tanx(where−3π ≤x≤3π )andy=cotx(where6π ≤x≤23π ).$

The area bounded by $y=x_{2},y=[x+1],0≤x≤2$ and the y-axis is where $[.]$ is greatest integer function.

The area bounded by the curves $y=g_{e}xandy=(g_{e}x)_{2}$ is

The area made by curve $f(x)=[x]+x−[x] $ and x-axis when $0≤x≤n(n∈N)$ is equal to { where [x] is greatest integer function}