Evaluate the integral: ∫12∫02𝑥−𝑥2(𝑥2+𝑦2)−1/2𝑑𝑦𝑑𝑥Group of answer choices2+ln⁡(2+1)ln⁡|sec⁡𝜃+tan⁡𝜃|+𝐶2−ln⁡(2+1)ln⁡(2−1) PreviousNext

Evaluate the integral: ∫12∫02𝑥−𝑥2(𝑥2+𝑦2)−1/2𝑑𝑦𝑑𝑥Group of answer choices2+ln⁡(2+1)ln⁡|sec⁡𝜃+tan⁡𝜃|+𝐶2−ln⁡(2+1)ln⁡(2−1) PreviousNext

If 𝑢 = 𝑥2 tan−1 𝑦𝑥 − 𝑦2 tan−1 𝑥𝑦 show that 𝜕2𝑢𝜕𝑥𝜕𝑦 = 𝑥2−𝑦2𝑥2+𝑦2 and 𝜕2𝑢𝜕𝑥𝜕𝑦 = 𝜕2𝑢𝜕𝑦𝜕𝑥.

If 𝑣 = 𝑟𝑚, where 𝑟2 = 𝑥2 + 𝑦2 + 𝑧2, then prove that 𝑣𝑥𝑥 + 𝑣𝑦𝑦 + 𝑣𝑧𝑧 = 𝑚(𝑚 + 1)𝑟𝑚−2.

Find the area of the region above the x-axis, included between the parabola 𝑦2=𝑎𝑥 and the circle 𝑥2+𝑦2=2𝑎𝑥.

Evaluate ∫0𝜋/2∫02𝑦sin⁡𝑦𝑑𝑥𝑑𝑦4𝑦2−𝑥2Group of answer choices𝜋/2𝜋/6𝜋/4−𝜋/2 PreviousNext