Grade 12 · Math · Calculus

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

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Antiderivatives of e^x, 1/x and trig

Grade 12 Math Worksheet

NameDate

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

Esme evaluates ∫ from π/6 to π/2 of 8 cos x dx. What is it?
Jun evaluates ∫ from π/6 to π/2 of 10 cos x dx. What is it?
Kira evaluates ∫ from π/2 to π/6 of 3 cos x dx. What is it?
4.
Which is ∫ (e^(4x)) dx, for Noah?
- (1/4)e^(4x) + C
- 4e^(4x) + C
- e^(4x + 1)/(4x + 1) + C
5.
Which is ∫ (eˣ − 4/x) dx, for Ren?
- eˣ⁺¹/(x + 1) − 4 ln|x| + C
- eˣ + 4/x² + C
- eˣ − 4 ln|x| + C
6.
Which is ∫ (6e^(2x)) dx, for Zee?
- 6e^(2x + 1)/(2x + 1) + C
- 3e^(2x) + C
- 12e^(2x) + C
Tala writes ∫ 8 cos(4x) dx = a·sin(4x) + C. What is a?
Pia writes ∫ 15 cos(5x) dx = a·sin(5x) + C. What is a?
Bo writes ∫ 9 cos(2x) dx = a·sin(2x) + C. What is a?
Ari writes ∫ 12 cos(3x) dx = a·sin(3x) + C. What is a?

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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