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Show that the area of the region bounded...

Show that the area of the region bounded by `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` (ellipse) is `pi` ab. Also deduce the area of the circle `x^(2)+y^(2)=a^(2)`

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The correct Answer is:
`piab`
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NCERT TELUGU-APPLICATION OF INTEGRALS-Miscellaneous Exercise
  1. Show that the area of the region bounded by (x^(2))/(a^(2))+(y^(2))/(b...

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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 = |3| and evaluate int(-6)^(0)|x+3|dx .

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  6. The area of the region bounded by the curve y=sinx, x-axis in [0,2pi] ...

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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 v=x, the x-axis and the ordinates x = -2 and...

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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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