Grade 12 · Math · Calculus

12th grade Evaluate definite integrals worksheet

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Evaluate definite integrals

Grade 12 Math Worksheet - Building Confidence

NameDate

Circle the best answer, or write your answer on the line.

Esme evaluates ∫ from 1 to 3 of (4x + 1) dx. What is it?
Jun evaluates ∫ from 1 to 2 of (6x − 2) dx. What is it?
Luz evaluates ∫ from −1 to 1 of (8x + 3) dx. What is it?
4.
Which line correctly starts ∫ from 1 to 3 of 2x dx, for Milo?
- [x²] from 1 to 3 = 9 − 1
- [2] from 1 to 3 = 2 − 2
- [x²] from 1 to 3 = 1 − 9
5.
Which line correctly starts ∫ from 1 to 2 of 3x² dx, for Noah?
- [6x] from 1 to 2 = 12 − 6
- [x³] from 1 to 2 = 8 − 1
- [x³] from 1 to 2 = 1 − 8
6.
Which line correctly starts ∫ from 0 to π/2 of cos x dx, for Ren?
- [sin x] from 0 to π/2 = 0 − 1
- [−sin x] from 0 to π/2 = −1 − 0
- [sin x] from 0 to π/2 = 1 − 0
Tala evaluates ∫ from 0 to 2 of x³ dx. What is it?
Pia evaluates ∫ from 0 to 4 of x³ dx. What is it?
Esme evaluates ∫ from 0 to 6 of x³ dx. What is it?
Jun evaluates ∫ from 0 to 3 of x³ dx. What is it?

12th grade Evaluate definite integrals worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Evaluate definite integrals: antiderivative at the top minus at the bottom. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can evaluate ∫ from a to b of f(x) dx as F(b) − F(a).
I can use e⁰ = 1, ln 1 = 0, sin 0 = 0 and cos 0 = 1 at the bottom end.
I can see that an odd function on [−a, a] integrates to 0.
I can find an unknown upper end from the value of an integral.

Standard: none (beyond CCSS)

Words to know

F(b) − F(a): The antiderivative at the top end minus at the bottom end.

bracket notation: [F(x)] from a to b means F(b) − F(a).

odd function: f(−x) = −f(x); its graph is the same after a half turn.

Common mistakes

Took F(bottom) − F(top). The rule is the top end minus the bottom end.

Found F at the top but did not subtract F at the bottom.

Took the derivative instead of the antiderivative.

Questions parents ask

What is the most common mistake with evaluate definite integrals?

Took F(bottom) − F(top). The rule is the top end minus the bottom end.

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More calculus

See all Calculus

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