Class 12

Math

Calculus

Application of Integrals

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$−x−y=1]˙$

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Find the area enclosed between the parabola $y_{2}=4ax$and the line $y=mx$.

Find the area of the parabola $y_{2}=4ax$bounded by its latus rectum.

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 bounded by the curves $y=x_{2}+2$, $y=x,x=0$and$x=3$.

Find the area of the region enclosed between the circles $x_{2}+y_{2}=1$ and $(x−1)_{2}+y_{2}=1$.

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

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

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).