Question

求求这个定积分怎么算，要详细过程，谢谢

Answer 1

∫(x->1 ) y√(1 x^2-y^2)dy
=1/2∫(x->1 ) √(1 x^2-y^2)dy^2
=-1/2∫(x-> 1)√(1 x^2-y^2)d(1 x^2-y^2)
=-1/2 *2/3 *√(1 x^2-y^2)^3 |(x->1)
=-2 (√(1个x^2-1) -√(1个x^2-x^2)
=-2√x^2 2
=2-2|x|(不知道x波段哪里没有绝对值)

Answer 2

∫dx = ∫[mv/(F-kv)]dv = (m/k)∫[kv/(F-kv)]dv
= (m/k)∫[(kv-F+F)/(F-kv)]dv = (m/k)∫[-1+F/(F-kv)]dv
= (m/k){-v - (F/k)∫[1/(F-kv)]d(F-kv)}
得 x = (m/k){-v - (F/k)ln(F-kv)}
= - (mF/k^2)ln(F-kv) - (m/k)v