Extra Credit – Bonus! Suppose that    and that we are asked to evaluate the integral  . Using your result from the last question, if    and ,  then which of the following is an accurate expression for I? Note that .

Extra Credit – Bonus! Suppose that    and that we are asked to evaluate the integral  . Which of the following expressions is the same as I?  Hint: Try performing the substitution   and see what happens when you simplify.

Suppose that we are asked to evaluate the definite integral   . Which of the following integrals is the same as I?

Explain how you would evaluate the following integral: 1. Do you apply a substitution (enter Y/N)? If yes, what is your u and du (enter functions or “N/A” without the quotes)? use-subst=[use-subst] u=[u] du=[du] 2. After your first step, can you evaluate the integral directly? If not, what integration method do you apply (enter the abbreviation from the short list of techniques below, without the quotes)? int-method=[int-method]. Integration method abbreviations: “DIRECT” – use a formula from our tables of known antiderivatives directly (no substitution) “USUB” – use integration by substitution “IBP” – use integration by parts “TSUB” – use trigonometric substitution “TRIG-IDENT” – use a secondary trigonometric identity “PF” – use partial fractions and integrate the resulting decomposition

Evaluate the following integral: .

Suppose that and are fixed real numbers. What is the value of the next limit (L)?   

Evaluate the following integral: .  

Evaluate the following definite integral by parts:  . u=[u] and du=[du] dv=[dv] and v=[v] Which of the following is the correct exact value of I? (Answer one of the capital letters A-E) [I-MC]               

We can write    where p and q are polynomials in x. What are these two polynomials (fill in the blanks of the polynomial coefficients)?  [px6]x^6+[px5]x^5+[px4]x^4+[px3]x^3+[px2]x^2+[px1]x+[px0]   [qx1]x+[qx0] Hint: For all real a and b we have that   .

Suppose that we are asked to evaluate the integral . After performing the substitution , which of the following expressions evaluates to I?