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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, y =4 and y= 0 into three equal parts.

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The parabolas y^(2) =4x and x^(2) =4y divide the square region bounded by the lines x=4,y=4 and the coordinates axes. If S_1 ,S_2, S_3 are the areas of these parts numbered from the top to bottom respectively,then-

NCERT BANGLISH-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. The area enclosed between y^(2) = x and y=x is:

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

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  5. 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 parabola 4y = 3x^(2) and the line 2y = 3...

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

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

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

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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 ...

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  17. Area bounded by the curve y=x^(3), the x-axis and the ordinates x = -2...

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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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