Question

求一道微积分题的答题步骤【定积分】

答案是二分之三，但是不知道步骤是怎样，求大神解答，可以发图，谢谢

Answer 1

最简单的方法：
∫tan(θ/2)*[sec(θ/2)]^2 *dθ

=∫2tan(θ/2)d[tan(θ/2)]
=[tan²(θ/2)]<π/2,π/3>
=[tan²(π/4)-tan²(π/6)]
=1-1/3=2/3

Answer 2

Answer 3

∫tan(θ/2)*[sec(θ/2)]^2 *dθ
=2*∫tan(θ/2) * [sec(θ/2)]^2 *d(θ/2)
=2*∫tan(θ/2) * d[tan(θ/2)]
=[tan(θ/2)]^2 |θ = π/3 →π/2
=[tan(π/4)]^2 - [tan(π/6)]^2
=1 - 1/3
=2/3

追问

请问下第二步最前面的数字2是不是从后面的dθ中提出来的？

追答

是的。可能是我变换的太快了！