class 12

Math

Calculus

Application of Integrals

The area (in sq. units) of the region described by ${(x,y):y_{2}≤2x$and $y≥4x−1}$is :

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Area lying between the curves $y_{2}=4x$and $y=2x$is(A) $32 $ (B) $31 $ (C) $41 $ (D) $43 $

The area bounded by the curve $y=x∣x∣$, x-axis and the ordinates $x=−1$and $x=1$is given by(A) 0 (B) $31 $ (C) $32 $ (D) $34 $[Hint : $y=x_{2}$if $x>0$and $y=−x_{2}$if $x<0$].

Find the area of the region bounded by the ellipse $4x_{2} +9y_{2} =1$

Using integration find the area of region bounded by the triangle whose vertices are $(1,0),(1,3)and(3,2)$.

The area of the figure bounded by the parabola $(y−2)_{2}=x−1,$ the tangent to it at the point with the ordinate y=3, and the x-axis is

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.

Consider two curves $C_{1}:y_{2}=4[y ]xandC_{2}:x_{2}=4[x ]y,$ where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines $x=1,y=1,x=4,y=4$ is $38 squ˙nits$ (b) $310 squ˙nits$ $311 squ˙nits$ (d) $411 squ˙nits$