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MATH1013 University Mathematics II

Assignment 4

Due date:  14 Nov, 2022  before 17:00

Please write down your name and university number. Precise and adequate explanations should be given to each problem.

1.  (2 points) Let f(x) be a continuous function satisfying 2xf(x )2 = f(x) for all real numbers

x. Compute

2

∫    f(t) dt.

(Hint: Find its derivative first.)

2.  Compute each of the following integrals or show that it is ∞ or −∞ .  (You should not write down the antiderivatives directly without explanations.)

1 − ln(lnx)

1                               − 1

(b)  (3 points)    (x + 1)tan    xdx

x5 + 6x4 + 15x3 + 24x2 + 24x + 7

(e)  (3 points)   ln xdx

(f)  (2 points)  xe−x2  dx