※ 引述《cverooo (台南南見鳥)》之銘言：
: http://i.imgur.com/IDF0UOW.jpg
: 跪求神手大大們
: 小弟願附上1500p解答贊助!!!
用到的公式
∫exp(at)dt = (1/a)exp(at) ---------- (1)
∫t^a dt = (1/(a + 1))t^(a + 1) --------(2)
1. 積分 = (6/(-3))t^(-3) + c (2)
= -2t^(-3) + c
2. 積分 = ∫[t^(-1/2) + t^(3/2)] dt
= 2t^(1/2) + (2/5)t^(5/2) + c (2)
3. 積分 = 25exp(t/5) - 10exp(t/10) + c (1)
4. 積分 = (4/7)x^(7/4) + c (2)
5. f'(x) = 10 - exp(0.05x)
f(x) = ∫f'(x) dx = 10x - 20exp(0.05x) + c
f(0) = 0 => c = 20
=> 利潤函數f(x) = 10x - 20exp(0.05x) + 20
6. f(x) = ∫(5x - x^2)dx = (5/2)x^2 - (1/3)x^3 + c (2)
f(1) = 3 = 5/2 - 1/3 + c
=> c = (18 - 15 + 2)/6 = 5/6
=> f(x) = (5/2)x^2 - (1/3)x^3 + 5/6
3 3
8. ∫1/x^2 dx = -1/x | = 2/3
1 1
2 2
9. ∫exp(-x/2) dx = -2exp(-x/2) | = -2exp(-1) + 2
0 0
2 2
10. ∫(3w^2 - 2w)dw = w^3 - w^2 | = 16
-2 -2
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