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Find the total area of the region between the curve and the x-axis. y = (x + 4)\sqrt x; 1 \leq...

Question:

Find the total area of the region between the curve and the x-axis.

{eq}y = (x + 4)\sqrt x; 1 \leq x \leq 9 {/eq}

a) 761

b) {eq}\frac{328}{3} {/eq}

c) 346

d) {eq}\frac{2492}{15} {/eq}

Area of the Region:

To compute the area of the region bounded by the curve and line we can use the vertical strip method with its formula {eq}\displaystyle A=\int_{a}^{b}ydx {/eq} where {eq}y {/eq} and {eq}dx {/eq} are the length and width of the rectangular strip.

Answer and Explanation:

Below is the graph,

Graph

The area of the region is,

{eq}\displaystyle A=\int_{1}^{9}ydx {/eq}

{eq}\displaystyle A=\int_{1}^{9}\left [ \left...

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How to Find Area Between Functions With Integration

from Math 104: Calculus

Chapter 14 / Lesson 3
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