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 inte…
Suppose we are asked to evaluate the following definite integral by substitution: . Answer the following questions: What is your initial substitution u=? What is the lower limit of integration after your substitution? What is the upper limit of integration after your substitution? What is an exact value for I=?
Suppose that we are asked to find the area (A) between the c…
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 ?
Suppose we are asked to evaluate the integral . If we set …
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 fol…
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 we are asked to evaluate the following integral: ….
Suppose we are asked to evaluate the following integral: . Select the appropriate choices to complete the next equivalent expressions for I: - .
Extra Credit – Bonus! Suppose the f and g are both continuo…
Extra Credit – Bonus! Suppose the f and g are both continuous and integrable functions on . Furthermore, say that we know that for all , . We say that the “fractional part” of x, denoted by , is the real or non-integer part of x belonging to . Also, we have that for all x. For example, , and so on. Now suppose that we want an expression for the following integral that does not involve the function f: . If we set , enter two exact (integer) expressions for the numerator and denominator of I: Numerator of I= Denominator of I=
Evaluate the following definite integral:
Evaluate the following definite integral:
Suppose that we want to evaluate the following integral: …
Suppose that we want to evaluate the following integral: Answer the following questions: Which u-sub to we choose first? u= What are the corresponding lower and upper limits of integration after the u-sub? and Which of the following methods do we use to evaluate the resulting integral after the substitution (type a capital single letter)? Integration by substitution Fundamental theorem of calculus Trigonometric substitution Partial fractions Integration by parts
4.2 Name each factor of production and their compensation….
4.2 Name each factor of production and their compensation. (4)