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In this lesson, we will learn how to determine the type of the improper integral with a discontinuous integrand and how to evaluate the integral if it is convergent.

Q1:

The integral οΈ π π π ο§ ο¦ l n d is convergent. What does it converge to?

Q2:

Consider the integral οΈ 1 π₯ π₯ 1 0 π d .

Find all possible values of π for which the integral is convergent.

Evaluate the integral for those values of π .

Q3:

The integral οΈ π β π π π 2 0 c o s s i n d is convergent. What does it converge to?

Q4:

Determine whether the integral οΈ π€ π€ β 2 π€ 5 0 d is convergent or divergent.

Q5:

Determine whether the integral οΈ 1 π₯ β π₯ β 2 π₯ 4 0 2 d is convergent or divergent.

Q6:

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

Q7:

The integral οΈ 1 β 1 β π₯ π₯ 1 0 2 d is convergent. What does it converge to?

Q8:

Determine whether the integral οΈ 1 π₯ π₯ 3 β 2 4 d is convergent or divergent.

Q9:

Consider the integral οΈ π₯ π₯ π₯ 1 0 π l n d .

Q10:

The integral οΈ 1 β π₯ β 1 π₯ 9 0 3 d is convergent. What does it converge to?

Q11:

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

Q12:

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

Q13:

The integral οΈ 1 β 5 β π₯ π₯ 5 0 3 d is convergent. What does it converge to?

Q14:

The integral οΈ π π₯ π₯ 0 β 1 3 1 π₯ d is convergent. What does it converge to?

Q15:

Determine whether the integral οΈ π π π 2 0 2 t a n d is convergent or divergent.

Q16:

The integral οΈ 1 β π₯ + 2 π₯ 1 4 β 2 4 d is convergent. What does it converge to?

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