Approximate area under a curve

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. Read this first

   Values of f (example values)

   x	f(x)
   0	3
   2	5
   4	9
   6	15

2. 1.

   Esme estimates the area under f from x = 0 to x = 6 with three rectangles, using left ends (see the table). What is the estimate?

   34
3. 2.

   Kira estimates the area under f from x = 10 to x = 25 with three rectangles, using left ends (see the table). What is the estimate?

   95
4. 3.

   Luz estimates the area under f from x = 0 to x = 1.5 with three rectangles, using left ends (see the table). What is the estimate?

   8.5
5. 4.

   Milo splits x = 0 to x = 6 into 3 equal strips for a left sum. Which heights does Milo use?

   • f(0), f(2), f(4)
   • f(1), f(3), f(5)
   • f(2), f(4), f(6)
6. 5.

   Noah splits x = 1 to x = 9 into 4 equal strips for a right sum. Which heights does Noah use?

   • f(3), f(5), f(7), f(9)
   • f(2), f(4), f(6), f(8)
   • f(1), f(3), f(5), f(7)
7. 6.

   Ren splits x = 2 to x = 10 into 4 equal strips for a left sum. Which heights does Ren use?

   • f(3), f(5), f(7), f(9)
   • f(2), f(4), f(6), f(8)
   • f(4), f(6), f(8), f(10)
8. 7.

   Zee splits x = 0 to x = 3 into 3 equal strips for a right sum. Which heights does Zee use?

   • f(0.5), f(1.5), f(2.5)
   • f(0), f(1), f(2)
   • f(1), f(2), f(3)
9. 8.

   Tala splits the interval from x = 1 to x = 9 into 4 equal strips. How wide is each strip?

   2
10. 9.

    Bo splits the interval from x = −3 to x = 5 into 4 equal strips. How wide is each strip?

    2
11. 10.

    Ari splits the interval from x = 3 to x = 8 into 10 equal strips. How wide is each strip?

    0.5