Grade 12 · Math · Calculus

12th grade Antiderivatives and the power rule worksheet

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Antiderivatives and the power rule

Grade 12 Math Worksheet - Challenge Me

NameDate

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

Esme's F(x) = ∫ (6x² − 4x + 5) dx, with C = 0. What is F(2)?
Kira's F(x) = ∫ (9x² − 6x + 2) dx, with C = 0. What is F(2)?
Luz's F(x) = ∫ (12x² + 4x + 7) dx, with C = 0. What is F(1)?
4.
Milo rewrites 3/√x as a power of x first. Which is ∫ 3/√x dx?
- 3√x + C
- −(3/2)x^(−3/2) + C
- 6√x + C
5.
Noah rewrites 4/x³ as a power of x first. Which is ∫ 4/x³ dx?
- −12/x⁴ + C
- −2/x² + C
- 4/x² + C
6.
Ren rewrites x^(2/3) as a power of x first. Which is ∫ x^(2/3) dx?
- (3/5)x^(5/3) + C
- (2/3)x^(−1/3) + C
- x^(5/3) + C
7.
Zee rewrites 5x√x as a power of x first. Which is ∫ 5x√x dx?
- 2x^(5/2) + C
- 5x^(5/2) + C
- (15/2)√x + C
8.
Which integral needs a rule other than the power rule, for Pia?
- ∫ 5/x dx
- ∫ 5√x dx
- ∫ 5/x² dx
9.
Which integral needs a rule other than the power rule, for Esme?
- ∫ (x² + 1)/x dx
- ∫ (x² + 1)/x² dx
- ∫ √x(x + 1) dx
10.
Which integral needs a rule other than the power rule, for Jun?
- ∫ 2/(3x²) dx
- ∫ 2∛x dx
- ∫ 2/(3x) dx

Antiderivatives and the power rule for integrals. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

indefinite integral: ∫ f(x) dx: the family of all antiderivatives, written with + C.

constant of integration: The + C: antiderivatives can differ by a constant.

power rule (integrals): ∫ xⁿ dx = xⁿ⁺¹/(n + 1) + C, for n ≠ −1.

Raised the power but did not divide by the new power. Check: the derivative must give back the original.

Divided by the old power instead of the new one, n + 1.

Took the derivative. An antiderivative goes the other way: the power goes up.

What is the most common mistake with antiderivatives and the power rule?

Raised the power but did not divide by the new power. Check: the derivative must give back the original.

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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