Area between parabola and ellipse 2

Calculus Level 3

What value of b b will ensure that the area between y = b x 2 y=bx^2 and x 2 9 + y 2 b 2 = 1 \frac{x^2}{9}+\frac{y^2}{b^2}=1 is equal to 3 3 ? Round your answer to 2 decimal places.


The answer is 2.31.

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1 solution

The two curves intersect in the first quadrant at a point whose x-coordinate is 0.9726183554749. The rest remains in integrating [(b/3)√(9-x^2)-b(x^2)] within the limits 0 to 0.9726183554749 and equating with (3/2) to get the value of b.

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