Class 12

Math

Calculus

Application of Integrals

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.

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Find the area of the region bounded by the curve $y_{2}=x$and the lines $x=1,x=4$and the x-axis.

Using integration find the area of the triangular region whose sides have the equations $y=2x+1$, $y=3x+1$ and $x=4$.

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

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 and find the area bounded by the curve $∣x∣ +∣y∣ =a andx_{2}+y_{2}=a_{2}(wherea>0)$ If curve $∣x∣+∣y∣=a$ divides the area in two parts, then find their ratio in the first quadrant only.

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

Using the method of integration find the area bounded by the curve $∣x∣+∣y∣=1$.[Hint: The required region is bounded by lines $x+y=1,x−y=1,−x+y=1$and$−x−y=1]˙$

Sketch the graph of $y=∣x+3∣$and evaluate$∫−60∣x+3∣dx$.