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Cogito

Calculus · Chapter 8 · Lesson 2

Practice Worksheet

Evaluating Definite Integrals

Antiderivative at the top, minus at the bottom.

12 problems · about 22 minutes · FUN-6.A, FUN-6.B

NameDate

Figure — use these to answer the problems

Drag the two edges together and the shaded area vanishes. An integral from a point to itself is zero.
-8-8-6-6-4-4-2-222446688
y = 1x² + 0x + 0
  • Point(0, 0)
  • Second point(2, 4)
  • Slope between them2
a1
Lower limit0
Upper limit2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. Integral of 3x² from 1 to 3, antiderivative x³. Value?

    Answer

  2. Why does a definite integral need no + C?

    • It appears in both terms and cancels in the subtraction.
    • Because C is always zero.

  3. Integral of 2x from 0 to 4, antiderivative x². Value?

    Answer

  4. Integral of 3x² from 0 to 2, antiderivative x³. Value?

    Answer

  5. Integral of 2x from 1 to 3, antiderivative x². Value?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Integral of 4 from 0 to 5, antiderivative 4x. Value?

    Answer

  2. An integral from 2 to 7 is 12. What is it from 7 to 2?

    Answer

  3. Integral from 0 to 3 is 5, and from 3 to 8 is 4. What is it from 0 to 8?

    Answer

Stretch Yourself

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

4 problems

  1. Which statements about definite integrals are true?

    • Area below the axis counts as negative
    • Swapping the limits negates the value
    • The answer needs a plus C
    • The value is always positive
    • Tick every box that applies.

  2. Integral of 2x from 0 to 5, antiderivative x². Value?

    Answer

  3. The Evaluation

    Integral of 2x from 0 to 3. An antiderivative is x². What is the value?

    Answer

  4. The Same Point

    Integral of any function from 5 to 5. What is the value?

    Answer