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Prove that the curves y^2 = 4x, x^2 = 4y...

Prove that the curves `y^2 = 4x, x^2 = 4y`, divide the area of the square bounded by `x = 0, x= 4, y = 4, y = 0` into three equal parts.

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PRADEEP PUBLICATION-APPLICATIONS OF INTEGRALS-EXERCISE
  1. Using the method of integration find the area of the region bounded by...

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  2. (a) Using integration, find the area of the region bounded by the tria...

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  3. Prove that the curves y^2 = 4x, x^2 = 4y, divide the area of the squar...

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  4. Compute the area enclosed by the curves y= 2^x and y = log2x between t...

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  5. Compute the area enclosed by the curves y = e^x and y = logex between ...

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  6. Find the area enclosed by the lines y = 0, y= x, x= 1, x=2.

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  7. Compute the area shown shaded in the figure.

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  8. Find the area enclosed by the curves x= sqrty , y=0 and x= sqrt2.

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  9. Compute the area shown shaded in the figure.

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  10. Find the area bounded by the curves y = sqrt(1-x^2) and y = 0.

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  11. Find the area bounded by the lines x= 0, y= 0 and x+y = 1.

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  12. Find the area shown shaded in the figure

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  13. Find the area shown shaded in the figure

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  14. Find the area bounded by the curves y =e^x, x= 0, y= 0 , x= 1.

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  15. Find the area bounded by the curves y = logex, x,y=0 and x=e.

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  16. Find the area enclosed between the curve y= sqrt(x-1), the x-axis and ...

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  17. Find the area enclosed betweenn y = sin x and the x-axis from x= 0 to ...

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  18. (i) Determine the area under the curve y=sqrt(a^2-x^2) included betwee...

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  19. Find the area of the region bounded by the curve y = x, and the lines ...

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  20. Find the area of the region bounded by y^2 = 9x , x = 2,x = 4 and the ...

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