Clicker Question 1 What is ? – A. 1 / (1 + x 2 ) + C – B. x / (1 + x 2 ) + C – C. sin( ) – D. (1 + x 2 ) + C – E. (1 + x 2 ) / x + C

Clicker Question 2 What is ? – A. 3/2 – B. / 6 – C. 10 / (9 3) – D. / / (9 3) – E. 5 / 3

Clicker Question 3 How do you feel about trig integrals and trig substitutions? – A. Love em! ( Right Answer!) – B. – C. Whats trig?

Partial Fraction Technique Recall what a rational function is. Question: It is possible to anti-differentiate any rational function? Answer: Theoretically, yes! – If top has higher (or =) power than the bottom, divide, getting whole and fractional parts. – Factor the bottom into linears and quadratics. – Separate each factor out using partial fraction technique. – Integrate each part using u-subs or trig subs.

A simple example (1/(x 2 – 3x – 4))dx – Factor the denominator. – Write A/(x – 4) + B/(x + 1) = 1/(x 2 – 3x – 4) and solve for A and B. – Now we have two separate integrals we can solve.

Two More Examples (x 3 / (x 2 +1))dx – This is an improper fraction. So divide first! ((x + 2)/(x 3 + x))dx – If, after factoring, a factor of the denominator is quadratic (as opposed to linear), we need to put Ax + B above it, not just A.

Assignment for Monday Hand-in #1 is due at noon. Read Section 7.4. Do Exercises 7, 9, 11, 15 in that section.