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In this lesson, we will learn how to determine the type of an improper integral over an infinite interval and how to evaluate the integral if it is convergent.

Q1:

Determine whether the integral οΈ π π π β 0 π c o s s i n d is convergent or divergent.

Q2:

Determine whether the integral οΈ οΉ π¦ β 3 π¦ ο π¦ β β β 3 2 d is convergent or divergent.

Q3:

Determine whether the integral οΈ 1 3 β 4 π₯ π₯ 0 β β d is convergent or divergent.

Q4:

Determine whether the integral οΈ 1 β 1 + π₯ π₯ β 0 4 d is convergent or divergent.

Q5:

Determine whether the integral οΈ π₯ β 1 + π₯ π₯ β 0 2 3 d is convergent or divergent.

Q6:

Determine whether the integral οΈ πΌ πΌ β 0 2 s i n d is convergent or divergent.

Q7:

Determine whether the integral οΈ π₯ π₯ π₯ β 1 l n d is convergent or divergent.

Q8:

The integral οΈ 2 π 0 β β π d is convergent. What does it converge to?

Q9:

The integral οΈ π£ π£ + 2 π£ β 3 β 2 2 d is convergent. What does it converge to?

Q10:

The integral οΈ 1 π₯ + π₯ π₯ β 1 2 d is convergent. What does it converge to?

Q11:

The integral οΈ π§ π§ + 4 π§ 0 β β 4 d is convergent. What does it converge to?

Q12:

The integral οΈ 1 ( π₯ β 2 ) π₯ β 3 3 2 d is convergent. What does it converge to?

Q13:

The integral οΈ π₯ β π₯ + π₯ β π₯ β 1 d is convergent. What does it converge to?

Q14:

The integral οΈ π π β 2 β 5 π d is convergent. What does it converge to?

Q15:

The integral οΈ π₯ π π₯ β β β β π₯ 2 d is convergent. What does it converge to?

Q16:

The integral οΈ π§ π π§ 0 β β 2 π§ d is convergent. What does it converge to?

Q17:

The integral οΈ π π₯ π₯ β 1 β 2 1 π₯ d is convergent. What does it converge to?

Q18:

The integral οΈ π¦ π π¦ β 2 β 3 π¦ d is convergent. What does it converge to?

Q19:

The integral οΈ π π¦ β 0 β β π¦ d is convergent. What does it converge to?

Q20:

The integral οΈ π₯ π₯ π₯ β 1 2 l n d is convergent. What does it converge to?

Q21:

Consider the integral οΈ 1 ( 2 π₯ + 1 ) π₯ β ο§ ο© d .

Determine whether the integral is convergent or divergent.

Determine the value of integration.

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