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Find the curve such that the area of the...

Find the curve such that the area of the trapezium formed by the co-ordinate axes, ordinate of an arbitrary point & the tangent at this point equals half the square of its abscissa.

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The correct Answer is:
`y = cx^2 +-x`
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MOTION-DIFFERENTIAL EQUATION -Exercise 3
  1. The perpendicular from the origin to the tangent at any point on a cur...

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  2. Find the curve for which any tangent intersects the y-axis at the poin...

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  3. Find the curve such that the area of the trapezium formed by the co-or...

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  4. Find the equation of the curve passing through the origin if the middl...

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  5. A perpendicular drawn from any point P of the curve on the x-axis meet...

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  6. The equation of curve in which portion of y-axis cutoff between origin...

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  7. Find the orthogonal trajectories for the given family of curves when ‘...

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  8. The population P of a town decreases at a rate proportional to the num...

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  9. It is known that the decay rate of radium is directly proportional to ...

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  10. Let the function ln f(x) is defined where f(x) exists for x geq 2 an...

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  11. Find the differentiable function which satisfies the equation f(x)= -i...

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  12. Find all functions f(x) defined on (-pi/2,pi/2) with real values and h...

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  13. A tank contains 100 litres of fresh water. A solution containing 1 gm/...

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  14. A tank with a capacity of 1000 litres originally contains 100 gms of s...

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  15. (dy)/(dx)=y+int0^1 ydx given y=1 where x=0

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  16. Find the continuous function which satisfies the relation, int0^x t f(...

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  17. A curve passing through (1, 0) such that the ratio of the square of th...

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  18. The curve f(x) is given by

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  19. The curve g(x) is given by -

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  20. The value of int1^2(g(x) -f(x))dx is-

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