x∧2+(y-5)∧2=16绕x轴旋转求体积

Question

x∧2+(y-5)∧2=16绕x轴旋转 求体积

Answer 1

（定积分的应用）
所求环体的体积=∫[π(5+√(16-x²))²-π(5-√(16-x²))²]dx
=40π∫√(16-x²)dx
=40π∫4cost*4costdt (令x=4sint)
=320π∫[1+cos(2t)]dt (应用倍角公式)
=320π[t+sin(2t)/2]│
=320π(π/2-0)
=160π²