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In this lesson, we will learn how to express definite integrals as Riemann sums and to evaluate the limit of a Riemann sum at infinity.

Q1:

Evaluate οΈ οΉ 4 π₯ β 4 π₯ ο π₯ 1 0 3 d by taking the limit of Riemann sums.

Q2:

Express l i m ο β β ο ο ο² ο§ ο ο ο¨ 1 π ο 5 4 β ο» ο as a definite integral.

Q3:

Express οΈ οΌ 2 π₯ β 5 π₯ ο π₯ 5 2 2 d as the limit of Riemann sums.

Q4:

Express οΈ 3 5 π₯ π₯ 2 π 0 s i n d as the limit of Riemann sums.

Q5:

Using Riemann sums, express l i m π β β π π = 1 5 6 ο β π π as an integral.

Q6:

Evaluate οΈ ( β π₯ β 4 ) π₯ 2 β 4 d using the limit of Riemann sums.

Q7:

Evaluate οΈ οΉ π₯ β 3 π₯ β 5 ο π₯ 2 β 4 2 d using the limit of Riemann sums.

Q8:

Evaluate οΈ οΉ π₯ β 2 π₯ ο π₯ 1 0 2 3 d using the limit of Riemann sums.

Q9:

Evaluate οΈ οΉ π₯ β 5 π₯ ο π₯ 2 0 3 d by taking the limit of Riemann sums.

Q10:

Express l i m ο β β ο ο ο² ο§ ο ο ο¨ 1 π ο 1 3 + 5 ο» ο as a definite integral.

Q11:

Evaluate οΈ οΉ 5 π₯ β 5 π₯ ο π₯ 1 0 2 3 d using the limit of Riemann sums.

Q12:

Express οΈ οΌ 4 π₯ + 4 π₯ ο π₯ β 1 β 8 2 d as the limit of Riemann sums.

Q13:

Express οΈ οΌ 5 π₯ + 4 π₯ ο π₯ 5 4 2 d as the limit of Riemann sums.

Q14:

Express οΈ οΌ 2 π₯ + 2 π₯ ο π₯ β 2 β 6 2 d as the limit of Riemann sums.

Q15:

Express οΈ οΌ 4 π₯ + 4 π₯ ο π₯ 6 1 2 d as the limit of Riemann sums.

Q16:

Evaluate οΈ ( β π₯ β 4 ) π₯ 6 β 4 d using the limit of Riemann sums.

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