Page 1 of 3
Download
Get this sheet
SubscriptionOpen any sheet in any course, up to 40 a month, keys included. Or $40 month to month.
$25/mo, billed yearly
SubscribeTry one first: a free Chapter 1 worksheet (PDF, no sign-in).
What's on the worksheet
- Evaluate each integral by reading it as a signed area.\int_{-3}^{4} (-5)\,dx\int_{-2}^{4} (6 - x)\,dx\int_{3}^{3} \left(x^2 + 7\right)dx\int_{-6}^{0} \sqrt{36 - x^2}\,dx\int_{5}^{1} 4\,dx
- Let $f
- Complete the square under each root to recognize part of a circle, sketch the region, then evaluate.
- Use symmetry.
- Jin runs a window-washing platform that moves up and down the side of a tall hotel.
- The graph of f on [-4, 6] is shown.
Teach it first
The free lesson teaches it with worked examples and practice problems.
Signed area and integrals from geometry: the lesson ›More Chapter 7 worksheets: Riemann sums and the definite integral
- 7.1Approximating area with Riemann sums
- 7.2The trapezoidal rule and Simpson's rule
- 7.3The definite integral as a limit of Riemann sums
- 7.4Signed area and integrals from geometry
- 7.5Properties of definite integrals