# 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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**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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**Q18: **

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

**Q19: **

Determine .

**Q20: **

Determine .

**Q22: **

Find , given that is a constant.

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