The area bounded by y=4-x2 and y=0,y=3 is

# The area bounded by $y=4-{x}^{2}$ and $y=0,y=3$ is

1. A

$\frac{16}{3}$

2. B

$\frac{22}{3}$

3. C

$\frac{26}{3}$

4. D

$\frac{28}{3}$

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### Solution:

The given curve is $y=4-{x}^{2}$ and the lines are $y=0,y=3$

$y=0⇒x=±2$ and $x=0⇒y=4$

The rough skectch is as below

The required area is area of shaded region

The shaded area is double the area of the region bounded by the curve $x=\sqrt{4-y}$, the lines $y=0,y=3$ and $y-$ axis.

Hence, the required area is $A=2{\int }_{0}^{3}\sqrt{4-y}dy$

it gives

Therefore, the required area is

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