答案是1 + (x - π/2)/2
具体步骤如下:
0 <= x <= π/2,
∫_{0}^{x}f(t)dt = ∫_{0}^{x}sin(t)dt = 1 - cos(x)
π/2 ≤ x ≤ π,
∫_{0}^{x}f(t)dt = ∫_{0}^{π/2}f(t)dt + ∫_{π/2}^{x}f(t)dt
= ∫_{0}^{π/2}sin(t)dt + ∫_{π/2}^{x}dt/2
= 1 + (x - π/2)/2
常用积分公式:
1)∫0dx=c
2)∫x^udx=(x^(u+1))/(u+1)+c
3)∫1/xdx=ln|x|+c
4)∫a^xdx=(a^x)/lna+c
5)∫e^xdx=e^x+c
6)∫sinxdx=-cosx+c
7)∫cosxdx=sinx+c
8)∫1/(cosx)^2dx=tanx+c
9)∫1/(sinx)^2dx=-cotx+c
10)∫1/√(1-x^2) dx=arcsinx+c