Class 12

Math

Calculus

Area

Find the area bounded by $y=∣∣ sinx−21 ∣∣ andy=1forx∈[0,π]$

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

Let $A_{r}$ be the area of the region bounded between the curves $y_{2}=(e_{−kr})x(wherek>0,r∈N)and the liney=mx(wherem=0)$, k and m are some constants $A_{1},A_{2},A_{3},…$ are in G.P. with common ratio

Find the area bounded by the curve $xy_{2}=4(2−x)$ and y-axis.

If $(a,0)$, agt 0, is the point where the curve $y=sin2x−3 sinx$ cuts the x-axis first, A is the area bounded by this part of the curve, the origin and the positive x-axis. Then

Consider $f(x)={cosx(2π −x)_{2} 0≤x<2π 2π ≤x<π $ such that f is periodic with period $π$. Then which of the following is not true?

Match the following lists :

If the curve $y=ax_{1/2}+bx$ passes through the point (1,2) and lies above the x-axis for $0≤x≤9$ and the area enclosed by the curve, the x-axis, and the line x=4 is 8 sq. units. Then

Let $A_{r}$ be the area of the region bounded between the curves $y_{2}=(e_{−kr})x(wherek>0,r∈N)and the liney=mx(wherem=0)$, k and m are some constants $n→∞lim i=1Σ n A_{i}=48(e_{2k}−1)1 $ then the value of m is