Definite integrals and net area
Grade 12 Math Worksheet - Building Confidence
Circle the best answer, or write your answer on the line.
From x = 0 to x = 10, Kira's graph of f encloses area 12 above the axis, then 5 below, then 4 above. What is ∫ from 0 to 10 of f(x) dx?
From x = 0 to x = 6, Luz's graph of f encloses area 7 above the axis, then 10 below, then 1 above. What is ∫ from 0 to 6 of f(x) dx?
On [0, 8], Milo's graph of f has area 10 above the axis and 4 below, and it ends below the axis. What is true about ∫ from 0 to 8 of f(x) dx?
- Positive, because 10 − 4 > 0
- It equals 14
- Negative, because f ends below the axis
On [0, 8], Noah's graph of f has area 3 above the axis and 9 below, and it ends above the axis. What is true about ∫ from 0 to 8 of f(x) dx?
- Negative, because 3 − 9 < 0
- Positive, because f ends above the axis
- It equals 12
On [0, 8], Ren's graph of f has area 7 above the axis and 7 below, and it ends below the axis. What is true about ∫ from 0 to 8 of f(x) dx?
- Zero, because 7 − 7 = 0
- Negative, because f ends below the axis
- It equals 14
On [0, 8], Zee's graph of f has area 5 above the axis and 2 below, and it ends below the axis. What is true about ∫ from 0 to 8 of f(x) dx?
- Positive, because 5 − 2 > 0
- Negative, because f ends below the axis
- It equals 7
Tala draws f(x) = 4, a flat line. What is ∫ from 2 to 7 of 4 dx?
Pia draws f(x) = 3, a flat line. What is ∫ from 1 to 6 of 3 dx?
Bo draws f(x) = 5, a flat line. What is ∫ from −2 to 3 of 5 dx?
Ari draws f(x) = 1.5, a flat line. What is ∫ from 3 to 10 of 1.5 dx?