Class 12

Math

Calculus

Area

The area of the closed figure bounded by $x=−1,y=0,y=x_{2}+x+1$, and the tangent to the curve $y=x_{2}+x+1$ at A(1,3) is

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If $a(a>0)$ is the value of parameter for each of which the are of the figure bounded by the straight line $y=1+a_{4}a_{2}−ax $ and the parabola $y=1+a_{4}x_{2}+2ax+3a_{2} $ is the greatest, then the value of $a_{4}$ is ___

Match the statements given in List I with the values given in List II.

If the area bounded by the x-axis, the curve $y=f(x),(f(x)>0)and the linesx=1,x=bis equal tob_{2}+1 −2 for allb>1,$ then find f(x).

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 $C_{2},y=1,andx=π$. For the values of $α$, the area bounded by $C_{1},C_{2},x=0andx=π$ is

The area bounded by $y=sec_{−1}x,y=cosec_{−1}x,and linex−1=0$ is

The area of the region bounded by the curve $y=e_{x}$ and lines x=0 and y=e is

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

The area bounded by the curves $y=x(x−3)_{2}andy=x$ is ___ (in sq. units).