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Fundamental Theorem of Calculus - Printable Mathematics Worksheets - Wayground

Fundamental Theorem of Calculus

15 questions

11th Grade - University

Mathematics

The Fundamental Theorem of Calculus worksheet gives Grade 11–13 mathematics students focused practice applying definite integrals to calculus problems. Across 15 multiple-choice questions, students evaluate integrals, find the area under a curve over stated bounds, interpret a definite integral in terms of area, and work with results that may require exact values such as π. The set also includes a calculator question, reflecting the range of reasoning and computation used in integral evaluation. This free printable worksheet is useful for introducing, reinforcing, or checking students’ ability to connect antiderivatives with definite integrals and distinguish signed area from geometric area. Students select from plausible numerical and algebraic options, making it easier to identify errors involving limits of integration, signs, coefficients, or area interpretation. A complete answer key is included for efficient review, independent practice, homework, or formative assessment.

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Worksheets

Fundamental Theorem of Calculus

Total questions: 15

Name
Class
Date
1.
Evaluate the integral
a)
30/3
b)
31/3
c)
29/3
d)
32/3
2.
a)
12/3
b)
6.5
c)
5.5
d)
11/3
3.
Find the area under a curve defined by the equation 5x4+3x+7 between the x values 0 and 4.
a)
1200
b)
1/12
c)
1134
d)
1076
4.
a)
40
b)
32
c)
64
d)
Not possible
5.
a)
-1
b)
-2
c)
1/2
d)
-1/2
6.
Calculator Question
a)
(A)
b)
(B)
c)
(D)
d)
(E)
7.
a)
(A)
b)
(B)
c)
(C)
d)
(D)
8.
a)
(A)
b)
(C)
c)
(D)
d)
(E)
9.
Evaluate the Definite Integral 
a)
8π
b)
16π
c)
4π
d)
2π
10.
a)
1 ⁄ (1+x3) 
b)
(3x2) ⁄ (1+x3) 
c)
x3  ⁄ (1+x3) 
d)
HELP
11.
a)
A
b)
B
c)
C
d)
D
12.

Evaluate in terms of area

∫02 f(x) dx

a)

4

b)

-4

c)

4 + 2π

d)

-4 - 2π

13.
a)
12/3
b)
6.5
c)
5.5
d)
11/3
14.
a)
A
b)
B
c)
C
d)
D
15.
a)
A
b)
B
c)
C
d)
D
Answer Key

Fundamental Theorem of Calculus

Total questions: 15

1.
d) 32/3
2.
b) 6.5
3.
d) 1076
4.
b) 32
5.
a) -1
6.
c) (D)
7.
c) (C)
8.
d) (E)
9.
d) 2π
10.
b) (3x2) ⁄ (1+x3) 
11.
b) B
12.
b)

-4

13.
b) 6.5
14.
d) D
15.
c) C

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FAQs

What does this Fundamental Theorem of Calculus worksheet cover?

This worksheet uses 15 multiple-choice questions to assess applying the Fundamental Theorem of Calculus to definite integrals. Students evaluate integrals, calculate area under a curve between given x-values, interpret an integral as signed area, and select exact results such as values involving π.

How can I use this worksheet to teach the Fundamental Theorem of Calculus?

First review how an antiderivative is evaluated at the upper and lower limits, then model how that difference gives a definite integral. Use the worksheet’s area-under-a-curve and area-interpretation questions to discuss when an integral represents signed area rather than total geometric area, and have students explain why each option is correct or incorrect.

What mistakes should I watch for when students complete this worksheet?

Watch for students subtracting the endpoint values in the wrong order, applying an antiderivative incorrectly, or losing coefficients when evaluating a definite integral. In the area questions, students may also choose a positive geometric area when the graph-based integral is negative, or confuse a calculator result with the required exact value.

How do I assign and grade this Fundamental Theorem of Calculus worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key for all 15 multiple-choice questions. For printable submissions, you can scan student work with the Wayground for Teachers app to support faster grading. The PDF option can also help schools reduce screen time when appropriate.

How can I differentiate this definite-integral worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the integral notation, bounds, and multiple-choice options are easier to read. You can also enable a dyslexia-friendly font, or translate the worksheet’s written directions and answer choices into another language while keeping the calculus expressions visible.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support mastery of essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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