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Unformatted text preview: Quiz 1
Name: SID: Write clearly!
Question 1 Let f and g be twice continuously dierentiable functions. Then the integral
f (x)g (x)dx is equal to: (1) f (x)g (x) - f (x)g (x)dx, (2) f (x)g(x) - f (x)g(x)dx, (3) f (x)g (x) - f (x)g(x) + f (x)g(x)dx, (4) All of the above. (5) 1 and 3 are correct. (6) 2 and 3 are correct.
Question 2 Evaluate
tan6 (x)dx. Use the formulas:
1 + tan2 (x) = sec2 (x), (tan(x)) = sec2 (x), (sec(x)) = sec(x) tan(x). Hint : Do it in three steps. 1 2 Question 3 Show that the following formula
xn ex dx = xn ex - n xn-1 ex dx is correct. Question 4 Evaluate
1 e ln(x)dx. Show all the work. ...
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