Definite Integral Practice
This worksheet provides practice problems on definite integrals, including evaluation and applications.
Includes
Standards
Topics
Definite Integral Practice
Name:
Date:
Score:
Read each question carefully and show all your work. Simplify your answers where possible.
Evaluate the following definite integrals.
1. ∫ (from 0 to 2) (3x² - 4x + 1) dx
2. ∫ (from 1 to 3) (2/x) dx
3. Given ∫ (from 0 to 5) f(x) dx = 10 and ∫ (from 5 to 7) f(x) dx = 3, what is ∫ (from 0 to 7) f(x) dx?
7
13
30
Cannot be determined
Complete the statement of the Fundamental Theorem of Calculus (Part 1):
4. If F(x) is an antiderivative of f(x), then ∫ (from a to b) f(x) dx = .
5. Find the area under the curve y = x² from x = 0 to x = 3.
6. The definite integral of a function from a to b represents the net signed area between the function's graph and the x-axis.
True
False
7. A car's velocity (in m/s) is given by v(t) = 3t² - 2t. Find the total distance traveled by the car from t = 0 seconds to t = 2 seconds.
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.