Calculus 2 - HEA and VEA (VEA Example)

Timestamps: 00:00 Visualization and Introduction to HEA and VEA 06:55 Example Problem (From Quiz) 22:50 Full Solution of Problem with Sketch 23:10 Practice for yourself! Explanations made clear here! I assume that everyone knows how to graph and visualize basic equations, even if you don't, I explained how to still solve the area by integration without sketching the graph. 1st Step: List down the equations with respect to a variable, if there is a simpler approach, use that solution. In this case, I visualized that since x^2 is a curve that goes upwards, I'm already thinking VEA, therefore I manipulated the equations and turned them into functions of x "f(x)" or just "y" 2nd Step: Limits Limits can be found through multiple ways, in this method, by equating both equations equally (I know) we can find their INTERSECTING POINTS which means it is where the area is closed, if you look at the graph at the end of the video, you can see where the equations intersect. 3rd Step: We can identify the Upper and Lower Boundaries by substituting a value of our "x" in between our limits. We can identify it this way since when we substitute a value to it, we can plot the point on the cartesian plane and see which equation is at the Lower B. and Upper B. (See the sketch of the graph) 4th Step: "L" can be defined as the LENGTH OF THE RECTANGLE (Introduction Visualization). We can identify our "L" by equating L to UPPER BOUNDARY - LOWER BOUNDARY (L = UpB - LowB) which we knew what is what at the 3rd step. 5th Step: Solve the integral, be careful with the minus/negative sign when multiplying. Make sure to add parentheses on your polynomial when substituting. You just learned how to solve the area by integration (VEA)!!