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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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MODERN PUBLICATION-APPLICATIONS OF THE INTEGRALS-EXERCISE
  1. Find the area enclosed by the parabola 4y = 3x^2 and the line 2y = 3x+...

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  2. Find the area of the region bounded by the curve y^2 = 4x and the lin...

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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. Draw the diagram to show the area enclosed by the curves: y^2=16x and ...

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  5. AOBA is the part of the ellipse 9x^2+y^2=36 in the first quadrant such...

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  6. Calculate the area of the region enclosed between the circles : x^2 + ...

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  7. Draw a rough sketch of the following region and find the area enclosed...

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  8. Find the area bounded by y=1+2 sin^(2)x,"X-axis", X=0 and x=pi.

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  9. Is the parabola y^2=4x symmetrical about x-axis?

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  10. Is the circle x^2+y^2=r^2 symmetrical about the line y=x?

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  11. Find the area enclosed by the circle x^2+y^2=9.

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  12. Find the area of the semi-portion of the circle x^2+y^2=4

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  13. Find the area of the region bounded by (i) y=x^4, x=1,x=5 and x-axis.

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  14. Area lying in the first quadrant and bounded by the circle x^2 + y^2 =...

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  15. Area of the region bounded by the curve y^2=4x , y-axis and the line y...

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  16. Smaller area enclosed by the circle x^2+y^2 = 4 and the line x + y = ...

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  17. Area lying between the curve y^2 = 4x and the line y = 2x is :

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  18. Area bounded by the curve y = x^3, the x-axis and the ordinates x = –...

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  19. The area bounded by the curve y = x|x|,x-axis and the ordinates x=-1, ...

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  20. (a) (i)Find the area of the circle x^2+y^2=16, which is exterior to th...

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