Match the following profiles to the correct picture.

Choose the following malocclusion shown in this image.

Which trig sub do we use to evaluate the integral ?  

Suppose we are asked to evaluate the following indefinite integral:  . Which of the following selections correctly sketches the steps needed to evaluate this integral?

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)?