class 12

Math

Calculus

Application of Integrals

The area of the region enclosed by the curves $y=x,x=e,y=x1 $and the positive x-axis is

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

Find the area of the region lying in the first quadrant and bounded by $y=4x_{2},x=0,y=1$ and $y=4$.

Sketch the region common to the circle $x_{2}+y_{2}=16$ and the parabola $x_{2}=6y$. Also, find the area of the region, using integration.

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

Using integration, find the area of the region bounded by the line $2y=−x+8$,x-axis is and the lines $x=2$ and $x=4$.

Prove that the curves $y_{2}=4x$and $x_{2}=4y$divide the area of the square bounded by $x=0,x=4,y=4andy=0$into three equal parts.

The area of the circle $x_{2}+y_{2}=16$exterior to the parabola $y_{2}=6x$is(A) $34 (4π−3 )$ (B) $34 (4π+3 )$(C) $34 (8π−3 )$ (D) $34 (8π+3 )$

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