Josephood7

Consider the integral [math] If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral.

Consider the integral [math] If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral.

Consider the integral [math] If the integral is divergent, type an upper-case "D". Otherwise, evaluate the integral.

Use the Comparison Theorem to determine whether the following integral is convergent or divergent.

    ?    Convergent    Divergent      1. [math]

The integral [math] is improper for two reasons: the interval [math] is infinite and the integrand has an infinite discontinuity at [math]. Evaluate it by expressing it as a sum of improper integrals of Type 2 and Type 1 as follows: [math]

If the improper integral diverges, type an upper-case "D".

(a) Find the values of [math] for which the following integral converges: [math] Input your answer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all [math], type an upper-case "D" in every blank.

Values of [math] are in the interval   ,  

For the values of [math] at which the integral converges, evaluate it. Integral = 

(a) Find the values of [math] for which the following integral converges: [math] Input your answer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all [math], type an upper-case "D" in every blank.

Values of [math] are in the interval   ,  

For the values of [math] at which the integral converges, evaluate it. Integral = 

Find the value of the constant [math] for which the integral [math] converges. Evaluate the integral for this value of [math].

[math] 

Value of convergent integral =