Class 12

Math

Calculus

Application of Integrals

Find the area enclosed by the parabola $4y=3x_{2}$ and the line $2y=3x+12.$

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Let $f(x)=x_{3}+3x+2andg(x)$ be the inverse of it. Then the area bounded by $g(x)$ , the x-axis, and the ordinate at $x=−2andx=6$ is $41 squ˙nits$ (b) $34 squ˙nits$ $45 squ˙nits$ (d) $37 squ˙nits$

Sketch the region bounded by the curves $y=x_{2}andy=1+x_{2}2 $ . Find the area.

Area bounded by the curve $xy_{2}=a_{2}(a−x)$ and the y-axis is $2πa_{2} squ˙nits$ (b) $πa_{2}squ˙nits$ $3πa_{2}squ˙nits$ (d) None of these

Let $C$ be a curve passing through $M(2,2)$ such that the slope of the tangent at anypoint to the curve is reciprocal of the ordinate of the point. If the area bounded by curve C and lin x=2i s A ,t h e nt h e v a l u e of $23A $i s__

Find the area of the region bounded by the x-axis and the curves defined by $y=tanx(where−3π ≤x≤3π )$ and $y=cotx(where6π ≤x≤23x )$ .

The area of the region of the plane bounded by $max(∣x∣,∣y∣)≤1andxy≤21 $ is $21 +1n2squ˙nits$ (b) $3+1n2squ˙nits$ $431 squ˙nits$ (d) $1+21n2squ˙nits$

the area of region for which $0<y<3−2x−x_{2}$ and $x>0$ is

Determine the area enclosed by the curve $y=x_{3}$, and the lines $y=0,x=2$ and $x=4$.