Class 12

Math

Calculus

Application of Integrals

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

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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 $x<0$].

The area bounded by the y-axis, $y=cosx$and $y=s∈x$when $0≤x≤2π $is(A) $2(2−1 )$ (B) $2 −1$ (C) $2 +1$ (D) $2 $

Sketch the region common to the circle $x_{2}+y_{2}=16$ and the parabola $x_{2}=6y$. Also, find the area of the region, using integration.

Sketch the region lying in the first quadrant and bounded by $y=4x_{2}$, $x=0$, $y=2$ and $y=4$. Find the area of the region using integration.

the area between the curves $y=x_{2}$ and $y=4x$ is

Find the area of the region bounded by the curves $y_{2}=2y−x$ and the y-axis.

Sketch the region lying in the first quadrant and bounded by $y=9x_{2},x=0,y=1andy=4.$ Find the area of the region using integration.