Class 12

Math

Calculus

Application of Integrals

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

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Find the area of the region bounded by the line $y=3x+2$, the x-axis and the ordinates $x=1andx=1$.

Find the area of the region ${(x,y):y_{2}≤4x,4x_{2}+4y_{2}≤9}$

Area enclosed between the curves $∣y∣=1−x_{2}andx_{2}+y_{2}=1$ is $33π−8 $ (b) $3π−8 $ $32π−8 $ (d) None of these

Consider a square with vertices at $(1,1)(−1,1)(−1,−1)and(1,−1).$ Let S be the region consisting of all points inside the square which are nearer to the origin than to any edge. Sketch the region S and find its area.

If $f(x)=sinx,∀x∈[0,2π ],f(x)+f(π−x)=2,∀x∈(2π ,π)andf(x)=f(2π−x),∀x∈(π,2π),$ then the area enclosed by $y=f(x)$ and the x-axis is $πsqu˙nits$ (b) $2πsqu˙nits$ $2squ˙nits$ (d) $4squ˙nits$

Area of the region bounded by the curve $y_{2}=4x$, y-axis and the line $y=3$is(A) 2 (B) $49 $ (C) $39 $ (D) $29 $

In Figure, AOBA is the part of the ellipse $9x_{2}+y_{2}=36$in the first quadrant such that $OA=2andOB=6$. Find the area between the arc AB and the chord AB.

Using the method of integration find the area of the region bounded by lines:$2x+y=4,3x2y=6$and $x3y+5=0$