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First Fundamental Theorem worksheets

Evaluate polynomial, reciprocal-power, trigonometric and exponential definite integrals with exact endpoint values.

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Evaluate each definite integral exactly. Show an antiderivative and upper minus lower.

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Evaluate a definite integral exactly

Find an antiderivative F, evaluate F at both endpoints, then compute F(upper) − F(lower). The answer keys keep fractions, roots, logarithms and powers of e exact.

Learning objective

What this activity builds

Use antiderivatives and upper minus lower to evaluate definite integrals exactly.

Worked example

Evaluate the integral from 0 to 2 of 3x² dx.

[x³] from 0 to 2 = 8

An antiderivative is x³. Subtract its value at the lower endpoint from its value at the upper endpoint.

Teaching notes

Make the practice count

  • Write the antiderivative before substituting endpoints.
  • Keep logarithms, radicals and powers of e exact.
  • For reciprocal-power sums, check that the interval does not cross zero.

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Choose 8 or 16 problems and any mix of polynomial, reciprocal-power, trigonometric and exponential integrands.

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Math SheetNameScoreTeacherDateFirst Fundamental Theorem of CalculusEvaluate each definite integral exactly. Show an antiderivative and upper minus lower.1.216·x5+4·x4-5·x3+6·x2+2·x+3dx2.-2-15·x3+3·x2-4·x-6dx3.-30x4+4·x3+4·x2+x+5dx4.-4-53-5·x-1+3·x-2dx5.-112·518·3·sin3·xdx6.1-1-4·e2·xdx7.01-6·x3+3·xdx8.2-16·43·xdxmath-sheet.comPage 1 of 2
Math SheetNameScoreTeacherDateFirst Fundamental Theorem of CalculusEvaluate each definite integral exactly. Show an antiderivative and upper minus lower.9.-11-x5-2·x4-4·x3+xdx10.316·x4+3·x3-4·x2+x+6dx11.54·-53·5·cosxdx12.155·x2+2·x-5·x-4dx13.516·x-1-3·x-4dx14.-2-1-4·e2·xdx15.32-x3+x2dx16.-718·-112·5·sin3·xdxmath-sheet.comPage 2 of 2

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