Approximate area under a curve

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Esme estimates the area under f(x) = x² + 2 from x = 0 to x = 6 with 3 rectangles, using right ends. What is the estimate?

   124
2. 2.

   Jun estimates the area under f(x) = x² + 3 from x = 0 to x = 2 with 4 rectangles, using right ends. What is the estimate?

   9.75
3. 3.

   Kira estimates the area under f(x) = x² + 1 from x = 0 to x = 9 with 3 rectangles, using right ends. What is the estimate?

   387
4. 4.

   Luz estimates the area under f(x) = x² + 5 from x = 0 to x = 4 with 2 rectangles, using right ends. What is the estimate?

   60

5. Read this first

   Values of f (example values)

   x	f(x)
   0	12
   1	11
   2	9
   3	6
   4	3
   5	1
   6	0

6. 5.

   Noah estimates the area under f from x = 0 to x = 6 with three equal strips and midpoint heights (see the table). What is the estimate?

   36
7. 6.

   Ren estimates the area under f from x = 0 to x = 12 with three equal strips and midpoint heights (see the table). What is the estimate?

   212
8. 7.

   Zee estimates the area under f from x = 0 to x = 9 with three equal strips and midpoint heights (see the table). What is the estimate?

   84
9. 8.

   Tala estimates the area under f from x = 0 to x = 6 with three trapezoids (see the table). What is the estimate?

   29
10. 9.

    Bo estimates the area under f from x = 1 to x = 7 with three trapezoids (see the table). What is the estimate?

    58
11. 10.

    Ari estimates the area under f from x = 0 to x = 3 with three trapezoids (see the table). What is the estimate?

    19.5