# Worksheet: Definite Integrals as Limits of Riemann Sums

In this worksheet, we will practice interpreting a definite integral as the limit of a Riemann sum when the size of the partitions tends to zero.

Q1:

Express as the limit of Riemann sums.

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Q2:

Without evaluating the limit, express as a limit of Riemann sums.

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Q3:

Express as a definite integral on the interval .

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Q4:

Evaluate using the limit of Riemann sums.

Q5:

Express as a definite integral on the interval .

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Q6:

Express as the limit of Riemann sums.

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Q7:

Without evaluating the limit, express as a limit of Riemann sums.

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Q8:

Evaluate by taking the limit of Riemann sums.

Q9:

Using Riemann sums, express as an integral.

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Q10:

Express as the limit of Riemann sums.

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Q11:

Evaluate using the limit of Riemann sums.

Q12:

Express as a definite integral.

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Q13:

Evaluate using the limit of Riemann sums.

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Q14:

Express as the limit of Riemann sums.

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Q15:

Evaluate using the limit of Riemann sums.

Q16:

Evaluate using the limit of Riemann sums.

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Q17:

Evaluate using the limit of Riemann sums.

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Q18:

Evaluate using the limit of Riemann sums.

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