Grade 12 · Math · Calculus

12th grade Choose an integration method worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

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Choose an integration method

Grade 12 Math Worksheet - Challenge Me

NameDate

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

Ari sets u = ln x to evaluate ∫ from 1 to e² of (ln x)²/x dx. What is it?
Bo sets u = ln x to evaluate ∫ from 1 to e² of (ln x)³/x dx. What is it?
Esme sets u = ln x to evaluate ∫ from 1 to e² of (ln x)⁴/x dx. What is it?
Kira picks a method for ∫ from 0 to 1 of x/(1 + x²) dx. What is it, to the nearest hundredth?
Luz picks a method for ∫ from 0 to 1 of 1/(1 + x²) dx. What is it, to the nearest hundredth?
Milo picks a method for ∫ from 0 to 2 of 2x/(4 + x²) dx. What is it, to the nearest hundredth?
Noah picks a method for ∫ from 0 to 3 of 6/(9 + x²) dx. What is it, to the nearest hundredth?
8.
Pia splits (x + 1)/(x² + 1) into simpler pieces before integrating. Which is ∫ (x + 1)/(x² + 1) dx?
- (1/4) ln(x² + 1) + arctan x + C
- (1/2) ln(x² + 1) + C
- (1/2) ln(x² + 1) + arctan x + C
9.
Ren splits (x + 2)/(x² + 4) into simpler pieces before integrating. Which is ∫ (x + 2)/(x² + 4) dx?
- (1/4) ln(x² + 4) + arctan(x/2) + C
- arctan(x/2) + C
- (1/2) ln(x² + 4) + arctan(x/2) + C
10.
Tala splits (3 + x)/√(1 − x²) into simpler pieces before integrating. Which is ∫ (3 + x)/√(1 − x²) dx?
- 3 arcsin x + C
- 3 arcsin x − √(1 − x²) + C
- 3 arcsin x − 2√(1 − x²) + C

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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