Class 12

Math

Calculus

Application of Integrals

Find the area of the region bounded by the parabola $y_{2}=2x$ and straight line $x−y=4.$

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

Draw a rough sketch to indicate the region bounded between the curve $y_{2}=4ax$ and the line $x=3.$ also, find the area of this region.

The area bounded by the curve $y_{2}=8xandx_{2}=8y$ is $316 squ˙nits$ b. $163 squ˙nits$ c. $314 squ˙nits$ d. $143 squ˙nits$

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

The area enclosed by the curve $y=4−x_{2} ,y≥2 sin(22 xπ )$ , and the x-axis is divided by the y-axis in the ratio. (a) $π_{2}+8π_{2}−8 $ (b) $π_{2}+4π_{2}−4 $ (c)$π−4π−4 $ (d) $2π+π_{2}−82π_{2} $

Find the area of the region $R$ which is enclosed by the curve $y≥1−x_{2} $ and max ${∣x∣,∣y∣}≤4.$

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

Find the area enclosed by the curve $x=3cost,y=2sint$