# Worksheet: Properties of Definite Integrals

In this worksheet, we will practice using properties of definite integration, such as the order of integration limits, zero-width limits, sums, and differences.

Q1:

Suppose has absolute minimum value and absolute maximum value . Given that , which property of integrals allows you to decide between what two values must lie?

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• E

Q2:

Write in the form .

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• E

Q3:

If , determine the value of .

Q4:

If and , find .

Q5:

If and , find .

Q6:

The function is continuous on . Given and , what is ?

Q7:

The function is continuous on . Given and , what is ?

Q8:

The function is continuous on and satisfies . Determine .

Q9:

If and , determine the value of .

Q10:

If and , find

Q11:

Suppose that on , the values of lie in the interval . Between which bounds does lie?

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Q12:

The function is continuous on . Given and , what is ?

Q13:

The function is continuous on . Given and , what is ?

Q14:

The function is continuous on . Given and , what is ?

Q15:

The function is continuous on . Given and , what is ?

Q16:

The function is odd, continuous on , and satisfies . Determine .

Q17:

The function is even, continuous on , and satisfies and . Determine .

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• D

Q18:

If the even function is continuous over the interval , where , determine the value of .

Q19:

Determine .

Q20:

Determine .

Q21:

Evaluate .

• A0
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• E

Q22:

Find , given that is a constant.

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