Find the area of the region lying in the first quadrant and bounded by and contexto.140 3 years ago Solution: The area in the first quadrant is bounded by , and is represented by the shaded area ABCDA as sq. units.
![\begin{aligned} \therefore \operatorname{Area} A B C D &=\int^{1} x d x \\ &=\int^{4} \frac{\sqrt{y}}{2} d x \\ &=\frac{1}{2}\left[\frac{y^{\frac{3}{2}}}{3}\right.\\ &=\frac{1}{3}\left[(4)^{\frac{3}{2}}-1\right] \end{aligned}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bd1f4d7904d1270da0a4ab92ab0b1ee1_l3.png "Rendered by QuickLaTeX.com")
![=\frac13\mathrm[8-1]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2d7dc222ad188a3e123e04252f905536_l3.png "Rendered by QuickLaTeX.com")
