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?

Evaluate the following definite integral in terms of p:   

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]

Suppose we are asked to evaluate the integral . If we set   and , which of the following is an expression for I in terms of u and v (NOT x)? Hints: For all real x:    For all real x:    Is the sine function even or odd?

Suppose that and   are fixed real numbers. Consider the following two limits (L and L2):    AND . Statement: The two limits are equal? (True/False)

Suppose that we are asked to find the area (A) between the curves     and    on the interval . Which of the following plots shows the shaded area between the two curves on ?