Blog

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

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

Evaluate the following integral: .

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

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]               

Evaluate the following definite integral in terms of p:   

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   .

Evaluate the following integral: .  

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

Suppose we are asked to evaluate the following definite integral by substitution:  . Answer the following questions: What is your initial substitution u=? [u] What is the lower limit of integration after your substitution? [ua] What is the upper limit of integration after your substitution? [ub] What is an exact value for I=? [I]