Question

Can you please help me with this

Answer 1

Answer:

  $\displaystyle A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta$

Step-by-step explanation:

The shaded area is the area of the curve bounded by θ = π and θ = 7π/6.* A differential of area in polar coordinates is ...

  dA = (1/2)r^2·dθ

So, the shaded area is ...

   $\displaystyle\boxed{A=\dfrac{1}{2}\int_\pi^{\frac{7\pi}{6}}{(\cos{\theta}+\sin{2\theta})^2}\,d\theta}$

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* We found these bounds by trial and error using a graphing calculator to plot portions of the curve.