Grade 12 · Math · Calculus

12th grade Choose an integration method worksheet

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Choose an integration method

Grade 12 Math Worksheet

NameDate

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

1.
Ari picks a method and finds ∫ xe^(x²) dx. Which is it?
- (1/2)e^(x²) + C
- e^(x²) + C
- (x²/2)e^(x²) + C
2.
Esme picks a method and finds ∫ x/(x² + 4) dx. Which is it?
- (1/2) ln(x² + 4) + C
- ln(x² + 4) + C
- (x²/4) arctan(x/2) + C
3.
Jun picks a method and finds ∫ cos(4x) dx. Which is it?
- −4 sin(4x) + C
- 4 sin(4x) + C
- (1/4) sin(4x) + C
Kira evaluates ∫ from 0 to ln 3 of e^(2x) dx. What is it?
Milo evaluates ∫ from 0 to ln 5 of e^(2x) dx. What is it?
Noah evaluates ∫ from 0 to ln 6 of e^(2x) dx. What is it?
Pia evaluates ∫ from 0 to π/6 of 6 sin(2x) dx. What is it?
Ren evaluates ∫ from 0 to π/6 of 10 sin(2x) dx. What is it?
Tala evaluates ∫ from 0 to π/9 of 12 sin(3x) dx. What is it?
Zee evaluates ∫ from 0 to π/15 of 20 sin(5x) dx. What is it?

Choosing an integration method. Every version has 10 questions, and the answer key prints on the second page.

I can say which method an integral needs from its shape.
I can evaluate definite integrals by the power rule, substitution, exponentials and trig.
I can split a fraction and choose ln or arctan for each piece.

Standard: none (beyond CCSS)

strategy: Read the shape, then pick the rule.

change of limits: In a definite substitution, the limits become u-values.

split: Write one fraction as a sum of simpler fractions.

Chose substitution where the inside's derivative is not a factor.

Chose the arctan rule for a shape that is not a number over x² + a².

Chose long division where the top's power is lower than the bottom's, or there is no fraction.

What is the most common mistake with choose an integration method?

Chose substitution where the inside's derivative is not a factor.

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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