Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Let A ( θ ) = 1 2 ∫ 0 θ [ 2 ( 1 + cos φ ) ] 2 d φ A(\theta)=\dfrac{1}{2}\displaystyle\int_{0}^{\theta}\bigl[2\bigl(1+\cos\varphi\bigr)\bigr]^2\,d\varphi A ( θ ) = 2 1 ∫ 0 θ [ 2 ( 1 + cos φ ) ] 2 d φ
Mathematics
Problem Let A ( θ ) = 1 2 ∫ 0 θ [ 2 ( 1 + cos φ ) ] 2 d φ A(\theta)=\dfrac{1}{2}\displaystyle\int_{0}^{\theta}\bigl[2\bigl(1+\cos\varphi\bigr)\bigr]^2\,d\varphi A ( θ ) = 2 1 ∫ 0 θ [ 2 ( 1 + cos φ ) ] 2 d φ r = 2 ( 1 + cos θ ) r=2\bigl(1+\cos\theta\bigr) r = 2 ( 1 + cos θ ) φ \varphi φ 0 0 0 θ \theta θ 0 ≤ θ ≤ π 0\le\theta\le\pi 0 ≤ θ ≤ π θ \theta θ A ( θ ) A(\theta) A ( θ ) 3 π 4 \dfrac{3\pi}{4} 4 3 π π 2 \dfrac{\pi}{2} 2 π π \pi π 2 π 3 \dfrac{2\pi}{3} 3 2 π Browse the problem library