Question

Following region is bounded by functions $y=\frac{1}{2}x\text{and}y=\sqrt{x}$.

Express $\Omega$as type I or type II region. If $\Omega$is a type I region, what are

$a,b$? If $\Omega$is a type II region, what are $c,d$?

Short answer

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$y=\sqrt{x}\text{and}y=\frac{1}{2}x$

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 $\left[0,4\right]$

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 $\left[0,2\right]$.

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