Quiz 4 - Take home
Due : Wednesday Feb 24, 2016
Please hand in your quiz at the beginning of lecture on the due date
Please ”do not forget to write your name”
1. Let F (x) = x2
R e3x
−x
ln(t2 )dt. Find
d
dx F (x).
Hint: use the product rule!
2. Evaluate the following integrals:
(a)
R
θ sec2 (θ) dθ
(b)
R
sin x cos x ln(sin x) dx
(c)
R
ln(tan x)
sin x cos x
(d)
R
(e)
R
1
√
2
0
dx
x tan−1 (x2 ) dx
t2 ln2 (t) dt
Hint: Match the above integrals (a - e) with the following methods (A - E) to evaluate each integral !!!
For example the method to evaluate integral (a) is Integration by Part (E). Try to match (b - e) with
(A - D), then find the integrals !!!
(A) Two times Integration by Part
(B) Substitution Rule + Integration by Part
(C) Two Times Substitution Rule
(D) Substitution Rule + Integration by Part
(E) Integration by Part
Have a Great Break!