Question

大学高数，急！！

大学高数，急！！请详细说明答案，谢谢！！

Answer 1

万能公式 ∫R(sinx, cosx)dx
= ∫R[2u/(1+u^2), (1-u^2)/(1+u^2)]2du/(1+u^2)
凑幂公式
∫f(x^n)x^(n-1)dx = (1/n)∫f(x^n)dx^n
∫[f(x^n)/x]dx = (1/n)∫[f(x^n)/x^n]dx^n
∫(asinx+bcosx)dx/(psinx+qcosx)型，
设 asinx+bcosx = A(psinx+qcosx) + B(psinx+qcosx)'
降幂递推公式
I<n> = ∫(tanx)^ndx = (tanx)^(n-1)/(n-1) - I<n-2>
I<n> = ∫(sinx)^ndx = -cosx(sinx)^(n-1)/n + (n-1)I<n-2>/n
I<n> = ∫(cosx)^ndx = sinx(cosx)^(n-1)/n + (n-1)I<n-2>/n

Answer 2

设A为同一种颜色,B为全是黑球
P(B|A)=P(AB)/P(A)=P(B)/P(A)=[C(3,6)/C(3,11)]/{[C(3,5)+C(3,6)]/C(3,11)}
=C(3,6)/[C(3,5)+C(3,6)]=2/3