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1. Indefinite integrals (antiderivatives)
2. Definite integrals
3. Integration by substitution
4. Area between curves
5. Riemann sums and the trapezoidal rule

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Name ______________________Date ____________Score ____ / 12

Calculus practice

Indefinite integrals (antiderivatives) · 1–3

Find the indefinite integral.

Medium
1.∫(−5x3 + 6x2 − x − 8) dx
Medium
2.∫(4x3 + 7x2 + 2x + 7) dx
Medium
3.∫(−5x3 − 4x2 − 5x − 9) dx

Definite integrals · 4–6

Evaluate.

Medium
4.∫31 (−3x2 − 4x − 1) dx
Medium
5.∫1−1 (−6x2 + 8x − 2) dx
Medium
6.∫2−2 (3x2 − 6x − 3) dx

Integration by substitution · 7–8

Integrate using substitution.

Medium
7.∫2x(x2 − 3)4 dx
Medium
8.∫2x(x2 + 1)4 dx

Area between curves · 9–10

Find the area of the region enclosed by the two curves.

Medium
9.y = x2 + 2x − 7, y = 4x − 4
Medium
10.y = x2 − x − 6, y = 2x − 2

Riemann sums and the trapezoidal rule · 11–12

Approximate the area under the curve.

Medium
11.Approximate the area under f(x) = 3x2 + 3 from x = 2 to x = 12 with 5 strips, using a midpoint sum.
Medium
12.Approximate the area under f(x) = x2 + 6 from x = 0 to x = 10 with 5 strips, using a midpoint sum.

Answer key — Calculus practice

Indefinite integrals (antiderivatives)

1.−54x4 + 2x3 − 12x2 − 8x + C
2.x4 + 73x3 + x2 + 7x + C
3.−54x4 − 43x3 − 52x2 − 9x + C

Definite integrals

4.−44
5.−8
6.4

Integration by substitution

7.15(x2 − 3)5 + C
8.15(x2 + 1)5 + C

Area between curves

9.323
10.1256

Riemann sums and the trapezoidal rule

11.1740
12.390

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