Chapter 13: Q 13. (page 1014)

Following region is bounded by functions $y = \frac{1}{2} x and y = \sqrt{x}$ .
Express $Ω$ as type I or type II region. If $Ω$ is a type I region, what are
$a, b$ ? If $Ω$ is a type II region, what are $c, d$ ?

Short Answer

Expert verified

For type I region, $a = 0, b = 4$

For type II region, $c = 0, d = 2$

Step by step solution

Given Information

The given curves are $y = \sqrt{x} and y = \frac{1}{2} x$

Simplification

It may be considered as either type I or type II.

When type I, it is bounded by $y = \frac{1}{2} x$ below and $y = \sqrt{x}$ for all $x$ in interval $[0, 4]$

Hence, for type I region, $a = 0, b = 4$

When region is expressed and type II, it is bounded by $y = \sqrt{x}$ to left and $y = \frac{1}{2} x$ for all $y$ in interval $[0, 2]$ .

Hence, for type II region $c = 0, d = 2$

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Following region is bounded by functions $y = \frac{1}{2} x and y = \sqrt{x}$ .
Express $Ω$ as type I or type II region. If $Ω$ is a type I region, what are
$a, b$ ? If $Ω$ is a type II region, what are $c, d$ ?

Short Answer

Step by step solution

Given Information

Simplification

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Following region is bounded by functions y=12xandy=x.Express Ωas type I or type II region. If Ωis a type I region, what area,b? If Ωis a type II region, what are c,d?

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Step by step solution

Given Information

Simplification

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Following region is bounded by functions $y = \frac{1}{2} x and y = \sqrt{x}$ .
Express $Ω$ as type I or type II region. If $Ω$ is a type I region, what are
$a, b$ ? If $Ω$ is a type II region, what are $c, d$ ?