Verified Answer :

meerkat18

The equation r = square root of theta can be translated into a semi-circle through the simplification to r^2 = theta. When theta is 0, r is zero. When r is -3pi/2, r2 is equal to 9/4 pi^2. The area of the semi-circle is equal to pi r^2 /2. Hence the area is equal to 34.88 units^2

Answer:

\(1.519\pi\)

Step-by-step explanation:

For any polar curve area of the region under the curve

\(\frac{1}{2} \int\limits^a_b {r^2} \, dt\)

Here r is given as

\(r=\theta \sqrt{\theta}\)

Hence area would be

\(\frac{1}{2} \int\limits^0_\frac{-3\pi}{2}  {theta}^{\frac{3}{2} }  \, d\theta \\=\frac{1}{2} \frac{2}{5}  {theta}^{\frac{5}{2} }\)

=\(=0.2(\frac{3\pi}{2} )^5\\=1.519\pi\)

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