# Find the area of the region bounded by the graphs of the given equations. y = 3, y = (square root...

## Question:

Find the area of the region bounded by the graphs of the given equations. {eq}y = 3, \: y = \sqrt[4]{x}, \: x = 0. {/eq}

## Finding the Area Between Two Curves:

To find the area bounded by the graphs of {eq}x = 0, \: y = c, \: y = f(x), {/eq} where {eq}f(x) \leq c, {/eq} we first calculate the intersection point where {eq}f(x) = c. {/eq} Call the solution {eq}x_1. {/eq} If this value is greater than zero, then the area between the two graphs is

{eq}A = \displaystyle\int_0^{x_1} c - f(x) \: dx. {/eq}

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The intersection of these two curves occurs when {eq}\sqrt[4]{x} = 3, {/eq} so {eq}x = 81. {/eq} Therefore the area between the curves is equal to

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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.