Let be a positive real number. The parabolas defined by and intersect at the points and .

Prove that the area enclosed by the two curves is constant. Explain why.

**Solution**

First of all we note that

Hence,

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Let be a positive real number. The parabolas defined by and intersect at the points and .

Prove that the area enclosed by the two curves is constant. Explain why.

**Solution**

First of all we note that

Hence,