Grade 12 · Math · Calculus

12th grade Antiderivatives of eˣ, 1/x and trig worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Antiderivatives of e^x, 1/x and trig

Grade 12 Math Worksheet - Building Confidence

NameDate

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

Esme writes ∫ 6e^(3x) dx = a·e^(3x) + C. What is a?
Jun writes ∫ 10e^(2x) dx = a·e^(2x) + C. What is a?
Kira writes ∫ 12e^(4x) dx = a·e^(4x) + C. What is a?
Luz writes ∫ 7e^(0.5x) dx = a·e^(0.5x) + C. What is a?
5.
Which is ∫ cos x dx, for Milo's sheet?
- sin x + C
- −sin x + C
- sin x
6.
Which is ∫ sin x dx, for Noah's sheet?
- −cos x
- −cos x + C
- cos x + C
7.
Which is ∫ csc² x dx, for Zee's sheet?
- cot x + C
- −2csc² x cot x + C
- −cot x + C
Tala evaluates ∫ from 1 to e² of (3/x) dx. What is it?
Pia evaluates ∫ from 1 to e³ of (5/x) dx. What is it?
Ari evaluates ∫ from 1 to e² of (6/x) dx. What is it?

Antiderivatives of eˣ, 1/x and the trig functions, with a mixed review. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

inside number: The k in e^(kx) or the m in cos(mx).

arch: One hump of a sine wave between two zeros.

Multiplied by the number inside, as the chain rule does for derivatives. An antiderivative divides by it.

Did not divide by the number inside. Differentiating the answer would give an extra factor.

Used the wrong sign. The derivative of sin is cos, but the derivative of cos is −sin.

What is the most common mistake with antiderivatives of eˣ, 1/x and trig?

Multiplied by the number inside, as the chain rule does for derivatives. An antiderivative divides by it.

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.

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