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Cogito

AP Calculus AB · Chapter 6 · Lesson 1

Practice Worksheet

The Definite Integral as Accumulation

Adding up infinitely many thin pieces.

11 problems · about 25 minutes · AP Calculus AB 6.1, 6.6, 6.7

NameDate

Figure — use these to answer the problems

Move the two ends and watch the shaded area change.

y = 1x² + 0x + 0

Point(0, 0)
Second point(3, 9)
Slope between them3

a1

b0

c0

Left end0

Right end3

Figure 1

Warm Up

Straightforward practice. Get the method working first.

4 problems

Integrate 2x from 0 to 6.
Answer
Integrate 2x from 0 to 5.
Answer
Integrate 3 from 0 to 4.
Answer
Integrate 3x² from 0 to 2.
Answer

Build It Up

The same ideas with more to keep track of.

3 problems

Integrate 2x from 3 to 3.
Answer
6
Select every true statement about the definite integral.
- Area below the axis counts as negative.
- It can never be zero unless the function is zero.
- Swapping the limits flips the sign.
- It measures the length of the curve.
- Tick every box that applies.
Integrate 2x from 4 to 0. What is the value?
Answer

Stretch Yourself

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

4 problems

An antiderivative of 4x³ is x⁴. Integrate from 0 to 2.
Answer
Integrate 5 from 2 to 7.
Answer
The Antiderivative
Integrate 2x from 0 to 4. What is the value?
Answer
Signed Area
Integrate x from −2 to 2. What is the value?
Answer