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Find area bounded by the curve sqrt(x) +...

Find area bounded by the curve `sqrt(x) +sqrt(y) =sqrt(a)` & coordinate axes.

Text Solution

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`sqrtx+sqrty=sqrta`
`sqrty=sqrta-sqrtx`
`y=(sqrta-sqrtx)^2`
`y=a+x-2sqrtasqrtx`
`A=int_0^a(a+x-2sqrtasqrtx)dx`
`=int_0^aadx+int_0^axdx-2sqrtaint_0^a x^(1/2)dx`
`=a[x]_0^a+[x/2]_0^a-2sqrta[2/3x^(3/2)]_0^a`
`=a^2+a^2/2-4/3a^(3/2+1/2)`
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