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Understanding Area Between Curves: Integration Techniques for Polynomials

This guide covers integration techniques for finding the area between two curves defined by functions f(x) and g(x). It highlights the importance of determining the limits of integration by finding the intersections of the curves. The process requires calculating areas both above and below the x-axis separately when necessary. The relationship between a function and its derivative is discussed, emphasizing the power rule for polynomials. By the end of this guide, you will understand how to compute areas effectively using integral calculus.

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Understanding Area Between Curves: Integration Techniques for Polynomials

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  1. Remember to change sign to + if area is below axis. Remember to work out separately the area above and below the x-axis . f(x) g(x) b A= ∫ f(x) - g(x) dx Integration is the process of finding the AREA under a curve and the x-axis a Area between 2 curves Finding where curve and line intersect f(x)=g(x) gives the limits a and b Integration of Polynomials IF f’(x) = axn Then I = f(x) =

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