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Prove that the curves y^(2) = 4x and x^(...

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

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NCERT TAMIL-APPLICATION OF INTEGRALS-Miscellaneous Exercise
  1. Prove that the curves y^(2) = 4x and x^(2) = 4y divide the area of the...

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  2. Find the area under the given curves and given lines: (i) y = x^(2),...

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  3. Find the area between the curves y = x and y = x^(2).

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  4. Find the area of the region lying in the first quadrant and bounded by...

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  5. Sketch the graph of y = |x + 3| and evaluate int(-6)^(0)|x + 3| dx.

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  6. Find the area bounded by the curve y = sin x between x = 0 and x = 2pi...

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  7. Find the area enclosed between the parabola y^(2) = 4ax and the line y...

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  8. Find the area enclosed by the parbola 4y=3x^(2) and the line 2y = 3x +...

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  9. Find the area of the smaller region bounded by the ellipse (x^(2))/(9)...

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  10. Find the area of the smaller region bounded by the ellipse (x^(2))/(a^...

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  11. Find the area of the region enclosed by the parabola x^(2) = y and the...

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  12. Using the method of integration find the area bounded by the curve |x|...

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  13. Find the area bounded by curves {(x,y): y ge x^(2) and y = |x|}

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  14. Using the method of integration find the area of the triangle ABC, coo...

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  15. Using the method of integration find the area of the region bounded by...

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  16. Find the area of the region {(x,y): y^(2) le 4x, 4x^(2) + 4y^(2) le 9...

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

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  18. The area bounded by the curve y = x^(3), x-axis and the ordinates: x =...

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  19. The area of the circle x^(2) + y^(2) = 16 exterior to the parabola y^(...

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  20. The are a bounded by the y-axis, y = cos x and y sin x when 0 le x le ...

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