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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