Class 11

Math

Calculus

Application of Integrals

If $A_{1},A_{2},A_{3},..$are sets such that $n(A_{i})=101−i$, $A_{1}⊃A_{2}⊃A_{3}⊃…⊃A_{100}$ and $A=∩_{i=5}A_{i}$ then n(A) is equal to

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Prove that the curves $y_{2}=4x$and $x_{2}=4y$divide the area of the square bounded by $x=0,x=4,y=4andy=0$into three equal parts.

The area enclosed by the curves $xy_{2}=a_{2}(a−x)$ and $(a−x)y_{2}=a_{2}x$ is

Find the area of the smaller region bounded by the ellipse $a_{2}x_{2} +b_{2}y_{2} =1$and the line $ax +by =1$

Find the area bounded by the curve $x_{2}=4y$and the line $x=4y_{2}$.

Area bounded by the curve $y=x_{3}$, the x-axis and the ordinates $x=2$and $x=1$is(A) $−9$ (B) $4−15 $ (C) $415 $ (D) $417 $

The area bounded by the x-axis, the curve $y=f(x),$ and the lines $x=1,x=b$ is equal to $b_{2}+1 −2 $ for all $b>1,$ then $f(x)$ is $x−1 $ (b) $x+1 $ $x_{2}+1 $ (d) $1+x_{2} x $

Find the area bounded by $y=x_{3}−xandy=x_{2}+x˙$

Find the area bounded by the curve $y=sinx$ between $x=0$ and $x=2π$.