Class 12

Math

Calculus

Area

The area of the region enclosed between the curves $x=y_{2}−1andx=∣x∣1−y_{2} $ is

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

If $A_{n}$ is the area bounded by y=x and $y=x_{n},n∈N,$ then $A_{2}.A_{3}…A_{n}=$

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___.

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

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

Sketch the region bounded by the curves $y=x_{2}andy=1+x_{2}2 $. Find the area.

If the area bounded by the curve $y=x_{2}+1$ and the tangents to it drawn from the origin is A, then the value of 3A is __.

Sketch the region bounded by the curves $y=5−x_{2} andy=∣x−1∣$ and find its area.