Choose an integration method

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Esme sets u = ln x to evaluate ∫ from 1 to e² of (ln x)⁴/x dx. What is it?

   32/5
2. 2.

   Jun sets u = ln x to evaluate ∫ from 1 to e² of (ln x)⁵/x dx. What is it?

   32/3
3. 3.

   Kira picks a method for ∫ from 0 to 1 of x/(1 + x²) dx. What is it, to the nearest hundredth?

   0.35
4. 4.

   Luz picks a method for ∫ from 0 to 1 of 1/(1 + x²) dx. What is it, to the nearest hundredth?

   0.79
5. 5.

   Milo picks a method for ∫ from 0 to 2 of 2x/(4 + x²) dx. What is it, to the nearest hundredth?

   0.69
6. 6.

   Noah picks a method for ∫ from 0 to 3 of 6/(9 + x²) dx. What is it, to the nearest hundredth?

   1.57
7. 7.

   Pia splits (x + 1)/(x² + 1) into simpler pieces before integrating. Which is ∫ (x + 1)/(x² + 1) dx?

   • (1/2) ln(x² + 1) + arctan x + C
   • (1/4) ln(x² + 1) + arctan x + C
   • (1/2) ln(x² + 1) + C
8. 8.

   Ren splits (x + 2)/(x² + 4) into simpler pieces before integrating. Which is ∫ (x + 2)/(x² + 4) dx?

   • arctan(x/2) + C
   • (1/4) ln(x² + 4) + arctan(x/2) + C
   • (1/2) ln(x² + 4) + arctan(x/2) + C
9. 9.

   Tala splits (3 + x)/√(1 − x²) into simpler pieces before integrating. Which is ∫ (3 + x)/√(1 − x²) dx?

   • 3 arcsin x − 2√(1 − x²) + C
   • 3 arcsin x + C
   • 3 arcsin x − √(1 − x²) + C
10. 10.

    Zee splits (x² + x + 1)/(x² + 1) into simpler pieces before integrating. Which is ∫ (x² + x + 1)/(x² + 1) dx?

    • x + C
    • x + (1/2) ln(x² + 1) + C
    • x + (1/4) ln(x² + 1) + C