# What is the area enclosed by f(x) = {x^2} / {2} + 1 and g(x) = x + 1?

## Question:

What is the area enclosed by {eq}f(x) = \frac{x^2}{2} + 1 \ and \ g(x) = x + 1? {/eq}

## Area of the Region Enclosed by Curves:

Consider two curves defined by {eq}y = f(x) {/eq} and {eq}y = g(x) {/eq}. Furthermore, suppose that these curves intersect on the points {eq}x = a {/eq} and {eq}x = b. {/eq} Also, suppose that {eq}f(x)\ge g(x) {/eq} for any {eq}x\in[a,b] {/eq} Then the area of the region enclosed by the two curves can be determined by solving the integral

{eq}\int_a^b f(x)-g(x) dx. {/eq}

## Answer and Explanation:

For the region enclosed by {eq}f(x) = \frac{x^2}{2} + 1 \ and \ g(x) = x + 1 {/eq}, we shall first determine the point where they intersect. To do...

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from Basic Geometry: Help & Review

Chapter 10 / Lesson 8