Choose an integration method

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   Ari looks at ∫ 2x(x² + 1)⁵ dx before starting. Which method fits it best?

   • the power rule on 2x and (x² + 1)⁵ separately
   • long division of 2x by x² + 1
   • the arctan rule on x² + 1
   • substitution with u = x² + 1
2. 2.

   Bo looks at ∫ 1/(x² + 25) dx before starting. Which method fits it best?

   • the power rule on (x² + 25)⁻¹
   • long division of 1 by x² + 25
   • the arctan rule with a = 5
   • substitution with u = x² + 25
3. 3.

   Esme looks at ∫ (x² + 1)/x dx before starting. Which method fits it best?

   • the power rule on x² + 1, then divide by x
   • the arctan rule on x² + 1
   • divide first, into x + 1/x
   • substitution with u = x² + 1
4. 4.

   Jun looks at ∫ 3x² − 4x + 7 dx before starting. Which method fits it best?

   • the arctan rule on 3x² − 4x + 7
   • divide 3x² − 4x + 7 by x first
   • substitution with u = 3x² − 4x + 7
   • the power rule, term by term
5. 5.

   Kira uses the power rule to evaluate ∫ from 1 to 3 of (3x² + 2) dx. What is it?

   30
6. 6.

   Milo uses the power rule to evaluate ∫ from −1 to 1 of (9x² + 4) dx. What is it?

   14
7. 7.

   Noah uses the power rule to evaluate ∫ from 2 to 3 of (12x² + 5) dx. What is it?

   81
8. 8.

   Pia sets u = x² + 1 to evaluate ∫ from 0 to 1 of 2x(x² + 1)² dx, changing the limits too. What is it?

   7/3
9. 9.

   Ren sets u = x² + 1 to evaluate ∫ from 0 to 2 of 2x(x² + 1)² dx, changing the limits too. What is it?

   124/3
10. 10.

    Zee sets u = x² + 3 to evaluate ∫ from 0 to 1 of 2x(x² + 3)² dx, changing the limits too. What is it?

    37/3