Area Under The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II | Summary and Q&A

TL;DR

Learn how to find the area under a curve using definite integration, with a step-by-step example.

Key Insights

• ❓ Definite integration can be used to find the area under any curve.
• ❣️ The formula for finding the area depends on whether it's with respect to the x-axis or the y-axis.
• 😥 The limits of integration are determined by the starting and ending points of the region under the curve.
• 🆘 Drawing the graph of the curve helps visualize the problem and determine the direction of the curve and the y-axis.
• ⛔ The area under a curve is calculated by substituting the equation of the curve and the limits of integration into the integral formula.
• ❎ The area is always measured in square units.
• 🅰️ The process of finding the area under a curve can be applied to various types of functions.

Transcript

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Questions & Answers

Q: What are the two formulas used to find the area under a curve?

The two formulas used are integral y dx for finding the area with respect to the x-axis and integral x dy for finding the area with respect to the y-axis.

Q: How do you determine the limits of integration for finding the area under a curve?

The limits of integration are determined by identifying the starting and ending points of the region under the curve. In the given example, the region starts at x = 0 and ends at x = 3.

Q: How do you draw the graph of a given function?

To draw the graph, identify the power of each variable in the equation. The variable with the minimum power will determine the direction of the curve. Also, determine the sign of the variable to determine the direction of the y-axis.

Q: What is the final answer to the example problem of finding the area under the curve y = x^2 from x = 0 to x = 3 with the x-axis?

The final answer is 9 square units.

Summary & Key Takeaways

• This video explains how to find the area under any curve using definite integral.

• It provides two formulas for finding the area: integral y dx for finding the area with respect to the x-axis, and integral x dy for finding the area with respect to the y-axis.

• A specific example is given to illustrate the process of finding the area under the curve y = x^2 from x = 0 to x = 3 with the x-axis.