Answer:
[tex]\frac{a^{2} }{6}[/tex] square units.
Step-by-step explanation:
The given curve is √x + √y = √a ......... (1)
Now, the curve intersects the x-axis at (a,0) point and the y-axis at (0,a) point.
Therefore, the are limited by equation (1) and the coordinate axes will be
= [tex]\int\limits^a_0 {(\sqrt{a} -\sqrt{x} )^{2} } \, dx[/tex]
= [tex]\int\limits^a_0 {a+x+2\sqrt{ax} } \, dx[/tex]
= [tex][ax + \frac{x^{2} }{2}+ 2\sqrt{a}\frac{x^{\frac{3}{2} } }{\frac{3}{2} } ]_{0} ^{a}[/tex]
= [tex]a^{2}+\frac{a^{2} }{2}- \frac{4a^{2} }{3}[/tex]
= [tex]\frac{a^{2} }{6}[/tex] square units. (Answer)
