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Cogito

AP Calculus AB · Chapter 8 · Lesson 1

Practice Worksheet

Area Between Curves

Top minus bottom, every time.

11 problems · about 24 minutes · AP Calculus AB 8.4, 8.5

NameDate

Figure — use these to answer the problems

Shade between two x values and read the accumulated area.
-8-8-6-6-4-4-2-222446688
y = 1x² + 0x + 0
  • Point(0, 0)
  • Second point(2, 4)
  • Slope between them2
a1
b0
c0
Left end0
Right end2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. y = 5 and y = 1 from 0 to 4. What is the area?

    Answer

  2. y = 4 and y = 0 from 0 to 3. What is the area?

    Answer

  3. y = x and y = 0 from 0 to 4. What is the area?

    Answer

  4. y = 6 and y = 2 from 0 to 5. What is the area?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A negative answer for an area means what? 1 for the order was wrong, 2 for the area is negative.

    Answer

  2. y = x² and y = 0 from 0 to 3. What is the area?

    Answer

  3. If two curves cross inside the interval, must you split the integral? 1 for yes, 0 for no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. y = 2x and y = 0 from 0 to 3. What is the area?

    Answer

  2. y = 10 and y = 4 from 1 to 3. What is the area?

    Answer

  3. The Crossings

    y = x and y = x² cross at x = 0 and at which other x?

    Answer

  4. Which Is On Top

    Between 0 and 1, which is greater at x = 0.5? 1 for x, 2 for x².

    Answer