1. ## integrals and area

whats the area between:
y=underroot(2x), y axis and the line y=4

ans:32/3
and area between x^2=4ay and its latus rectum

2. ## Re: integrals and area

You can get the upper bound for the first integral by solving $y = \sqrt{2x}$ for $y=4$. Then evaluate the integral and subtract it from a rectangle to get your answer.

Alternatively, you can get the answer directly by switching $x$ and $y$, rearranging to make $y$ the subject and integrating from 0 to 4. The curve will become a parabola, but it doesn't affect the integral.
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The latus rectum of $x^2 = 4ay$ is $y=a$.

If you shift the parabola down by $a$, we can integrate on the x-axis (the areas will still be the same). To get the bounds, find the x-intercepts of the new shifted parabola. Finally, take the absolute value of the integral to get the area.

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