Calculus 1 (0370)
Final Examination
2021/6/17 – 15:00~15:45
Notes:
1. Due to the particular conditions of this semester, online tests
will be real-time and open-book test. Please use your own
knowledge and not that of other people. Fraudulent copies
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your answer.
7. Send your copies by e-mail to
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0370-Final
YOUR NAME
YOUR STUDENT NUMBER
PAGE X/X
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those corresponding to your student number using the
following figure.
A, B, C, D, E, F, G
2 0 A B C D E F G
2 0 A B C D E F G
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Calculus 1 (0370)
Final Examination
2021/6/17 – 15:00~15:45
2 0 A B C D E F G
2 0 A B C D E F G
Problem 1 (75 pt). Calculate the following integrals.
(a)
cos 𝑥
𝑑𝑥
𝛼 sin 𝑥 + 𝛽 sin 𝑥
(10 pt.)
Take 𝛼 = 𝐀 + 𝐁 + 𝐂 and 𝛽 = 1 + 𝐄 + 𝐅 + 𝐆.
(b)
sec 𝛿𝑥 tan 𝛿𝑥 𝑑𝑥
(10 pt.)
Take 𝛿 = 𝐅 + 𝐆.
(c)
cos(𝑎𝑥) sin(𝑏𝑥) 𝑑𝑥
(10 pt.)
Take 𝑎 = 𝐀 and 𝑏 = 𝐀 − 𝐄 − 𝐅 − 𝐆.
(d)
𝑥+𝑎
𝑑𝑥
(𝑥 + 𝑏)
(15 pt.)
Take 𝑎 = 𝐀 and 𝑏 = 𝐀 − 𝐄 − 𝐅 − 𝐆.
(e)
𝑥 𝑒 𝑑𝑥
(15 pt.)
Take 𝑐 = 𝐀 + 𝐆.
(f)
𝑥
𝑑𝑥
cos 𝛾𝑥
Take 𝛾 = 𝐀 + 𝐅 + 𝐆.
(15 pt.)
Problem 2 (25 pt.) Find the area of the region 𝑅 bounded by
the curves 𝑦 = 𝑥 + 𝛿 and 𝑦 = 1 − 𝑥 between 𝑥 = 𝑎
and 𝑥 = 𝑏 . Take 𝛿 = 𝐅 + 𝐆 , 𝑎 = 𝐀 − 𝐄 − 𝐅 − 𝐆 and
𝑏 = 𝐀 + 𝐆.