When do you use a vertical and horizontal strip when finding areas between two curves in integral calculus?
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In integral calculus, you use vertical and horizontal strips to find areas between two curves depending on the orientation of the curves and how the problem is described.
1. Vertical Strips:
- Use vertical strips when the curves are defined as functions of x.
- When the curves are given by y = f(x) and y = g(x), and you integrate with respect to x, you can use vertical strips.
- In this case, the width of the strips is dx, and the height of each strip is f(x) - g(x).
2. Horizontal Strips:
- Use horizontal strips when the curves are defined as functions of y.
- When the curves are given by x = f(y) and x = g(y), and you integrate with respect to y, you can use horizontal strips.
- In this case, the width of the strips is dy, and the height of each strip is g(y) - f(y).
Remember, it's important to identify the orientation of the curves and write the integral accordingly to properly set up the integration for finding the area between two curves.
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