Find the area of the region enclosed by the functions. y=x^6 and y=8x^3

Question:

Find the area of the region enclosed by the functions.

{eq}y=x^6 \ {/eq} and {eq}\ y=8x^3 {/eq}

Computing Areas Using Integrals:

To solve this problem, we first look at the graph to determine the approach. Once we have the graph, we consider either a vertical strip or a horizontal strip. The choice of direction depends on the region in question. The area can then be represented by an integral. This integral is the Riemann sum of all such strips covering the area, so we can establish the integrand and the limits of integration using the information we have.

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We can make a sketch of the graph of the two curves to determine our approach. First, we note the points of intersection of the curves. This is done...

Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.