Area between curves | Applications of definite integrals | AP Calculus AB | Khan Academy

TL;DR

The area between two curves can be calculated by finding the definite integral of the difference between the two functions.

Transcript

• [Instructor] We have already covered the notion of area between a curve and the x-axis using a definite integral. We are now going to then extend this to think about the area between curves. So let's say we care about the region from x equals a to x equals b between y equals f of x and y is equal to g of x. So that would be this area right over h... Read More

Key Insights

• ❓ The area between two curves can be calculated by finding the definite integral of the difference between the two functions.
• ☺️ If one function is above the x-axis and the other is below, the area can still be calculated using the same method.
• 🤯 Even if both functions are below the x-axis, the area can be determined by taking the definite integral of the upper function minus the lower function.

Questions & Answers

Q: How can the area between two curves be calculated?

The area between two curves can be calculated by taking the definite integral of the upper function minus the lower function over the desired interval.

Q: What happens when one function is above the x-axis and the other is below?

In this case, the area between the curves can still be calculated using the same method. The integral of the upper function minus the lower function will yield the desired area.

Q: What if both functions are below the x-axis?

If both functions are below the x-axis, the integral of the upper function minus the lower function will still give the correct area. The negative values from the integral of the lower function will cancel out when subtracted by the integral of the upper function.

Q: Can this method be applied to any interval?

Yes, this method can be applied to any interval where the upper function is greater than the lower function. The area between the curves can be calculated by taking the definite integral of the difference between the two functions.

Summary & Key Takeaways

• The area between two curves can be found by taking the definite integral of the difference between the upper and lower functions.

• If both functions are above the x-axis, the area can be calculated by subtracting the definite integral of the lower function from the definite integral of the upper function.

• If one function is above the x-axis and the other is below, the area can still be calculated using the same method.