Area Between Two Curves

TL;DR

Learn how to find the area between two curves by taking the difference between their integral functions.

Transcript

in this video we're going to talk about how to calculate the area between two curves so let's go over the basics let's say we have some function f of x and we want to find the area under the curve from a to b so we're looking for the area of the shaded region the area is simply the definite integral from a to b of f of x dx now let's say if we have... Read More

Key Insights

• ❓ The area under a curve can be found by evaluating the definite integral of the function.
• 😘 The area between two curves can be calculated by subtracting the integral of the lower function from the integral of the upper function.
• 😀 The same method can be applied when dealing with curves in terms of y instead of x.
• ❣️ The choice of using x-values or y-values to evaluate the area depends on convenience.

Questions & Answers

Q: How do you calculate the area under a curve?

To find the area under a curve from a to b, you need to evaluate the definite integral of the function f(x) from a to b.

Q: How do you calculate the area between two curves?

To find the area between two curves, you subtract the integral of the lower function from the integral of the upper function, both evaluated from a to b.

Q: Can you use the y-values instead of x-values to calculate the area?

Yes, you can calculate the area using either the x-values or the y-values. Just make sure to use the appropriate integral function based on the axis of the bounded area.

Q: Will using the x-values or y-values yield different results when calculating the area?

No, using either the x-values or y-values to calculate the area will yield the same result. It is simply a matter of preference or convenience.

Q: How do you calculate the area when the curves are given in terms of y?

When the curves are given in terms of y, you can find the area by evaluating the definite integral of f(y) - g(y), where f(y) is the function on the right and g(y) is the function on the left, both integrated from c to d.

Summary & Key Takeaways

• To find the area under a curve from a to b, use the definite integral of the function f(x) from a to b.

• When finding the area between two curves, subtract the integral of the lower function from the integral of the upper function.

• Similarly, when dealing with functions in terms of y, use the definite integral of f(y) from c to d for x-axis bounded area and g(y) - f(y) for y-axis bounded area.

• Calculating the area can be done using either the x-values or the y-values, and both methods will yield the same result.