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!