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From an arbitrary point M(x,y) of the cu...

From an arbitrary point M(x,y) of the curve `y= x^(m) (m gt 0)` perpendiculars MN and ML `(x gt 0)` are dropped onto the coordinate axes. What part of the area of the rectangle ONML does the area ONMO constitute ?

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IA MARON-APPLICATIONS OF THE DEFINITE INTEGRAL-Computing Areas in Rectangular Coordinates
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  2. Find the area of the segment of the curve y^(2)= x^(3)-x^(2) if the li...

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  3. Determine the area of the figure bounded by two branches of the curve ...

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  4. Compute the area enclosed by the loop of the curve y^(2)=x (x-1)^(2)

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  5. Find the area enclosed by the loop of the curve y^(2) = (x-1) (x-2)^(2...

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  6. Find the area of the figure bounded by the parabola y= -x^(2) + 2x + 3...

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  7. Find the area bounded by the parabola y= x^(2) -2x + 2, the line tange...

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  8. We take on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2))=1 (a gt b)...

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  9. The area bounded between the parabola x^(2)=y/4 and x^(2)=9y and the s...

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  10. From an arbitrary point M(x,y) of the curve y= x^(m) (m gt 0) perpendi...

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  11. Prove that the areas S(0), S(1), S(2), .S(2),. S(3),….., bounded by th...

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  12. Find the areas enclosed between the circle x^(2) + y^(2)-2x + 4y-11=0 ...

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  13. Find the area of the region boun ded by curves f(x)=(x-4)^2,g(x)=16-x^...

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  14. Compute the area enclosed between the parabolas x= y^(2), x= (3)/(4)...

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  15. Compute the area enclosed by the curve y^(2)= (1-x^(2))^(3)

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  16. Compute the area enclosed by the loop of the curve 4(y^(2)-x^(2))+ x^(...

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  17. Compute the area of the figure bounded by the curve sqrtx + sqrty=1 an...

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  18. Compute the area of the figure enclosed by the curve y^(2) =x^(2) (1-x...

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  19. Compute the area enclosed by the loop of the curve x^(3) + x^(2) - y^(...

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  20. Compute the area bounded by the axis of ordinates and the curve x= y^(...

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