Class 12

Math

Calculus

Application of Integrals

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

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Find the area of the smaller part of the circle $x_{2}+y_{2}=a_{2}$cut off by the line $x=2 a $

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 $

Find the area bounded by curves ${(x,y):y≥x_{2}andy=∣x∣}$

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

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.

Find the area under the given curves and given lines:(i) $y=x_{2},$$x=1,x=2$and x-axis(ii) $y=x_{4}$, $x=1,x=5$and x-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.

Using the method of integration find the area of the triangle ABC, coordinates of whose vertices are A(2, 0), B (4, 5) and C (6, 3).