Class 12

Math

Calculus

Area

Consider curves $y=x_{2}1 ,y=4(x−1)1 .Letα$ be the value of $a(a>2)$ for which area bounded by curves between $x=2andx=ais1/aise_{2}+1andβbe the ofb∈(1,2),$ for which the area bounded by curves between x=b and $x=2is1−b1 ,$ then

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The ratio in which the line $x−1=0$ divides the area bounded by the curves $2x+1=4y+1 ,y=xandy=2$ is

The value of the parameter a such that the area bounded by $y=a_{2}x_{2}+ax+1,$ coordinate axes, and the line x=1 attains its least value is equal to

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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?

Find a continuous function f, where $(x_{4}−4x_{2})≤f(x)≤(2x_{2}−x_{3})$ such that the area bounded by $y=f(x),y=x_{4}−4x_{2},$ the y-axis, and the line $x=t,where(0≤t≤2)$ is k times the area bounded by $y=f(x),y=2x_{2}−x_{3},$ y-axis, and line $x=t(where0≤t≤2).$

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

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