Author Topic: Integration Question (Read 515 times) Tweet Share

wildareal · « **on:** July 16, 2010, 12:14:11 am »

A long trough whose cross-section is parabolic is 1 and a 1/2 metres wide at the top and 2 metres
deep. Find the depth of water when it is half-full.

/0 · « **Reply #1 on:** July 16, 2010, 01:48:52 am »

Situate the parabola so that the minimum is at (0,0), for convenience.

You want to find $h$ such that:
The area bounded by the parabola and $y=h$ is half of the area bounded by the parabola and $y=2$ .

First thing is to find the equation of the parabola, $y=f(x)$ .

Then

$\int_{-\frac{3}{4}}^\frac{3}{4} (h - f(x))\,dx = \frac{1}{2}\int_{-\frac{3}{4}}^\frac{3}{4} (2-f(x))\,dx$

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Author Topic: Integration Question (Read 515 times) Tweet Share

wildareal

Integration Question

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