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

Find the area of the region in the first quadrant enclosed by the x-axis, the line $y=x$, and the circle $x_{2}+y_{2}=32$.

The area inside the parabola $5x_{2}−y=0$ but outside the parabola $2x_{2}−y+9=0$ is $123 squ˙nits$ $63 squ˙nits$ $83 squ˙nits$ (d) $43 squ˙nits$

Find the area of the region bounded by the two parabolas $y=x_{2}$and $y_{2}=x$.

Find the area enclosed by the circle $x_{2}+y_{2}=a_{2}$.

If the area of bounded between the x-axis and the graph of $y=6x−3x_{2}$ between the ordinates $x=1$ and $x=a$ is $19$ units, then $a$ can take the value: (A) 4 or -2 (B) one value is in (2, 3) and one in (-1, 0) (C) one value is in (3, 4) and one in (-2,-1) (D) none of these

Find the area of the region bounded by the curve $y=x_{2}$and the line $y=4$.