Integrals and Areas Between Curves: Examples Part 5

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In this video I go over a useful example on finding the area between a curve by switching the variables to be functions of y as opposed to x. The example is finding the area enclosed by the line y = x + 1 and the parabola y2 = 2x + 6. Writing the functions in terms of y makes it easier to solve the integral without having to break up the function into 2 regions. This is a very important example so make sure to watch it!


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Integrals and Areas Between Curves: Examples Part 5

Integrals and Areas Between Curves Examples 5.jpeg

Example:

Find the area enclosed by the line y = x - 1 and the parabola y2 = 2x +6

Solution:

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If we stuck with using functions of x, then we would need to solve 2 integrals by breaking up y into 2 functions.

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