Area Between Curves Worksheet
A Grade 10 Math worksheet covering the calculation of area between curves using integration.
Includes
Standards
Topics
Area Between Curves
Name:
Date:
Score:
Read each question carefully and show all your work. Calculate the area between the given curves.
1. Find the area of the region bounded by the curves y = x² and y = x.
2. Calculate the area of the region enclosed by the parabolas y = x² and y = 2x - x².
3. To find the area between two curves, f(x) and g(x), where f(x) ≥ g(x) over an interval [a, b], we use the definite integral from a to b of dx.
4. The area between curves can sometimes be negative, indicating the lower function is above the upper function.
True
False
5. Which of the following represents the area between y = sin(x) and y = cos(x) from x=0 to x=π/2?
∫ (cos(x) - sin(x)) dx from 0 to π/2
∫ (sin(x) - cos(x)) dx from 0 to π/2
| ∫ (cos(x) - sin(x)) dx from 0 to π/2 |
∫ |cos(x) - sin(x)| dx from 0 to π/2
6. Determine the area of the region bounded by x = y² and x = y + 2.
Related Worksheets
Squeeze Theorem Practice
A worksheet for Grade 10 students to practice applying the Squeeze Theorem to determine limits of functions.
Derivative by Definition Worksheet
Understand and apply the definition of the derivative to calculate derivatives of various functions.
Implicit Differentiation Worksheet
A Grade 10 Calculus worksheet on implicit differentiation, covering finding derivatives of implicitly defined functions.
Curve Sketching Mastery
This worksheet provides exercises on curve sketching, focusing on identifying key features of functions and their graphs, suitable for Grade 10 Calculus students.
Extrema on a Graph: Calculus Worksheet
Explore the concepts of relative and absolute extrema of functions using graphical analysis for Grade 10 Calculus students.
First Derivative Test Worksheet
A worksheet for Grade 10 students covering the First Derivative Test, including finding critical points, intervals of increase and decrease, and local extrema.
Taylor Series Exploration
This worksheet introduces Grade 10 students to the concept of Taylor series, focusing on understanding polynomial approximations of functions.
Riemann Sums Worksheet
Explore the concept of Riemann sums to approximate the area under a curve, including left, right, and midpoint sums.