Definite Integral Practice

This worksheet provides practice problems on definite integrals, including evaluation and applications.

Grade 10 Math CalculusDefinite Integral

Use This Worksheet

Includes

2 Short AnswerMultiple ChoiceFill in the BlanksTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HS.C.A.1CCSS.MATH.CONTENT.HS.C.A.2

Topics

CalculusDefinite IntegralArea Under CurveAntiderivative

8 sections · Free to use · Printable

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?

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.