Integrals with inverse trig, long division and completing the square

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari evaluates ∫ from 0 to 2 of 8/(4 + x²) dx with the arctan rule. What is it, to the nearest hundredth?

   3.14
2. 2.

   Bo evaluates ∫ from 0 to 2 of 6/(4 + x²) dx with the arctan rule. What is it, to the nearest hundredth?

   2.36
3. 3.

   Esme evaluates ∫ from 0 to 5 of 10/(25 + x²) dx with the arctan rule. What is it, to the nearest hundredth?

   1.57
4. 4.

   Kira divides first and finds ∫ (x² + 3x + 5)/(x + 1) dx. Which is it?

   • (x³/3 + 3x²/2 + 5x)/(x²/2 + x) + C
   • x²/2 + 2x + C
   • x²/2 + 2x + 3 ln|x + 1| + C
5. 5.

   Milo divides first and finds ∫ (2x² + x)/(x + 1) dx. Which is it?

   • (2x³/3 + x²/2)/(x²/2 + x) + C
   • x² − x + C
   • x² − x + ln|x + 1| + C
6. 6.

   Noah divides first and finds ∫ (x³ + 2)/x dx. Which is it?

   • x³/3 + 2 ln|x| + C
   • (x⁴/4 + 2x)/(x²/2) + C
   • x³/3 + C
7. 7.

   Pia completes the square to evaluate ∫ from 1 to 3 of 1/(x² − 2x + 5) dx. What is it, to the nearest hundredth?

   0.39
8. 8.

   Ren completes the square to evaluate ∫ from −2 to 1 of 1/(x² + 4x + 13) dx. What is it, to the nearest hundredth?

   0.26
9. 9.

   Tala completes the square to evaluate ∫ from 3 to 7 of 1/(x² − 6x + 25) dx. What is it, to the nearest hundredth?

   0.2
10. 10.

    Zee completes the square to evaluate ∫ from 5 to 10 of 1/(x² − 10x + 50) dx. What is it, to the nearest hundredth?

    0.16