Question

Find the area of the shaded region in each of the following figures ?​

Answer 1

Answer:

A=2∫20(4−16−x2−−−−−−√)dx

A=16−∫2016−x2−−−−−−√)dx

From here, we can use integration by substitution...

Let x=4sinu

and dx=4cosudu

A=16−2∫π6016cos2udu

A=16−32[u2+sin2u4]∣∣π60

A=16−32(π12+3√8)

A=16−8π3−43–√

This can also be solved without calculus,

...but I should draw some pictures to illustrate, so I'll update my answer later to include the second method.

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Step-by-step explanation:

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