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Written Homework 5 – due in class 2/19

The following problems are selected from the suggested homework list.

1. Evaluate the following improper integrals. Do not apply Fundamental Theorem of Calculus to

improper integrals.

Demonstrate truncation, evaluation of the truncated integral, and compute the appropriate limit

of the evaluated proper integral.

For the evaluation of the proper truncated integral, compute the antiderivative manually without

the table. Then check your answer with the table. This is to practice both skills – integration

technique and using the table.

Z ∞

dz

a)

2 + 25

z

−∞

Z ∞ −y/a

ye

b)

dy for a > 0. Be sure to use l’Hopital’s rule when appropriate.

a

0

2. For the following improper integrals, use the ”end behavior” (or dominant behavior of the integrand near the singularity) to predict convergence. Be sure to specify the ”end behavior” and

explain your reasoning for your conclusion.

Z ∞

dθ

√

a)

θ2 + 1

1

Z 1

b)

(sin x)−3/2 dx (Hint: approximate sin x by its local linearization.)

0

1

Written Homework 5 – due in class 2/19

The following problems are selected from the suggested homework list.

1. Evaluate the following improper integrals. Do not apply Fundamental Theorem of Calculus to

improper integrals.

Demonstrate truncation, evaluation of the truncated integral, and compute the appropriate limit

of the evaluated proper integral.

For the evaluation of the proper truncated integral, compute the antiderivative manually without

the table. Then check your answer with the table. This is to practice both skills – integration

technique and using the table.

Z ∞

dz

a)

2 + 25

z

−∞

Z ∞ −y/a

ye

b)

dy for a > 0. Be sure to use l’Hopital’s rule when appropriate.

a

0

2. For the following improper integrals, use the ”end behavior” (or dominant behavior of the integrand near the singularity) to predict convergence. Be sure to specify the ”end behavior” and

explain your reasoning for your conclusion.

Z ∞

dθ

√

a)

θ2 + 1

1

Z 1

b)

(sin x)−3/2 dx (Hint: approximate sin x by its local linearization.)

0

1

…

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