Lesson Worksheet: Area under the Curve and Integration Mathematics

In this worksheet, we will practice using rectangles to estimate the area under the curve of a function and using a definite integral to find it.

Q1:

Evaluate 𝑥2𝑥𝑥d using the limit of Riemann sums.

  • A727
  • B16
  • C53
  • D12
  • E13

Q2:

Express 35𝑥𝑥sind as the limit of Riemann sums.

  • Alimsin6𝜋𝑛10𝜋𝑖𝑛
  • Blimsin6𝜋𝑛10𝜋𝑖𝑛
  • Climsin6𝜋𝑛10𝜋𝑖𝑛
  • Dlimsin6𝜋𝑛10𝜋𝑖𝑛
  • Elimsin6𝜋𝑛10𝜋𝑖𝑛

Q3:

Evaluate 𝑥3𝑥𝑥d using the limit of Riemann sums.

Q4:

Express 3𝑥𝑥d as the limit of Riemann sums.

  • Alim18𝑛3+6𝑖𝑛
  • Blim18𝑛3+6𝑖𝑛
  • Clim18𝑛36𝑖𝑛
  • Dlim18𝑛3+6𝑖𝑛
  • Elim18𝑛6𝑖𝑛

Q5:

Evaluate 𝑥𝑥d using the limit of Riemann sums.

  • A32
  • B20
  • C16
  • D20
  • E26

Q6:

Evaluate (𝑥4)𝑥d using the limit of Riemann sums.

Q7:

Express 2𝑥5𝑥𝑥d as the limit of Riemann sums.

  • Alim3𝑛22+3𝑖𝑛52+
  • Blim3𝑛23𝑖𝑛5𝑛3𝑖
  • Clim3𝑛22+3𝑖𝑛52+
  • Dlim3𝑛22+3𝑖𝑛52+
  • Elim3𝑛223𝑖𝑛52

Q8:

Evaluate 𝑥3𝑥5𝑥d using the limit of Riemann sums.

Q9:

Evaluate 4𝑥4𝑥𝑥d by taking the limit of Riemann sums.

Q10:

Without evaluating the limit, express 74𝑥𝑥d as a limit of Riemann sums.

  • Alim7𝑛745+7𝑖𝑛
  • Blim7𝑛745+7𝑖𝑛
  • Clim7𝑛745+7𝑖𝑛
  • Dlim7𝑛745+7𝑖𝑛
  • Elim7𝑛747𝑖𝑛

Practice Means Progress

Boost your grades with free daily practice questions. Download Nagwa Practice today!

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.