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Using integration find the area of th...

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

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y= 2x +1 is the line passing through `A(-1/2,0)` and B (0,1)
y=3x + 1 is the passing through `C(-1/3,0)` and B (0,1)
x= 4 is the parallel to y-axis and passing through D(4,0)
Required area= (area ODFB))-(area ODEB)
`=overset(4)underset(0)int (3x+1)dx -underset(0)overset(4)int (2x+1)dx`
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RS AGGARWAL-AREA OF BOUNDED REGIONS -Exercise 17
  1. Draw a rough sketch of the region {(x,y): y^2 le 3x,3x^2 + 3y^2 le16 }...

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  2. Draw a rough sketch and find the area of the region bounded by the par...

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  3. Find by intergraiton the area bounded by the curve y^2 = 4ax and the l...

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  4. Draw a rough sketch of the curve y=x/pi + 2 sin^2 x, and find the area...

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  5. Find the area bounded by the curve y=cos x between x=0 and x=2pi

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  6. Compare the areas under the curves y=cos ^2 x and y= sin ^2x between x...

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  7. Using integration find the area of the triangular region whose side...

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  8. Find the area of the region {(x,y) : x^2 le y le x }

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  9. Examples: Find the area of the region bounded by the curve y^2 = 2y - ...

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  10. Draw a rough sketch of the curves y=sin x and y= cos x as x varies fr...

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  11. Find the area of the bounded by the curve y^2 =2x+1 and the line x-y=1

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  12. Find the area bounded by the curve y=2x-x^2 and the straight line y=-x

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  13. Find the area of the region bounded by the curve (y-1)^2=4(x+1) and th...

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  14. Find the area of the region by the curve y=sqrt(x) and the line y=x

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  15. Find the are of the region included between the parabola y^2= 3x and t...

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  16. Find the area bounded by the curve y=cos x between x=0 and x=2pi

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  17. Find the area of the region in the first quadrant enclosed by the x-a...

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  18. Using integration, find the area of DeltaABC, whose vertices are A(2,3...

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  19. Using intergration find the area of the area of the triangle whose ver...

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  20. Using integration find the area of the triangular region whose side...

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