Find the area that bounded by the curve y =√x and the line x= 16​

Given equation of curve is y=

16−x

2

and the equation of line is X−axis i.e., y=0

∴

16−x

2

=0(i)

⇒16−x

2

=0

⇒x

2

=16

⇒x=±4

So, the intersection points are (4,0) and (−4,0).

∴ Area of curve, A=∫

−4

4

(16−x

2

)

1/2

dx

=∫

−4

4

(4

2

−x

2

)

dx

=[

2

x

4

2

−x

2

+

2

4

2

sin

−1

4

x

]

−4

4

=[

2

4

4

2

−4

2

+8sin

−1

4

4

]−[−

2

4

4

2

−(−4)

2

+8sin

−1

(−

4

4

)]

=[2.0+8.

2

π

−0+8.

2

π

]=8πsq units.

1 3 5

step-by-step explanation:

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