Find the area of the region bounded by the graph of the given equations

{eq}y=2x-x^2 , y= -5x{/eq}

Question:

Find the area of the region bounded by the graph of the given equations

{eq}y=2x-x^2 , y= -5x{/eq}

Area as Single Integrals

The area of the region bounded above by the graph of {eq}\displaystyle y=f(x), {/eq} and below by the graph {eq}\displaystyle y=g(x), {/eq} between {eq}\displaystyle x=a,x=b, {/eq} is given by

{eq}\displaystyle \int_a^b\left[f(x)-g(x)\right]\ dx. {/eq}

Sometimes, we need to find the points of intersection of the curves, by solving the system of the two equations of the curves.

Evaluating the integrals, we may need the following formula

{eq}\displaystyle \int x^n \ dx =\frac{1}{n+1}x^{n+1}+C, n\neq -1, C - \text{ constant}. {/eq}

Answer and Explanation: 1

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The region between the graphs {eq}\displaystyle y=2x-x^2, y=-5x, {/eq} is bounded by the two curves, between the points of intersection.

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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.


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