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Polynomial integration

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WorksheetWise · Standard · 1097

Polynomial integration

Work through each question. Show your reasoning where space is provided.

Name: ____________________ · Date: ____________

  1. 1. Find an indefinite integral of 32 x^3 + (5) with respect to x. Include the constant of integration.

  2. 2. Find an indefinite integral of 12 x^3 + (7) with respect to x. Include the constant of integration.

  3. 3. Find an indefinite integral of 24 x^3 + (0) with respect to x. Include the constant of integration.

  4. 4. Find an indefinite integral of 6 x^2 + (-5) with respect to x. Include the constant of integration.

  5. 5. Find an indefinite integral of 20 x^3 + (-2) with respect to x. Include the constant of integration.

WorksheetWise · en-au · 1/1

WorksheetWise · Standard · 1097

Polynomial integration — Answer key

Work through each question. Show your reasoning where space is provided.

  1. 1. Find an indefinite integral of 32 x^3 + (5) with respect to x. Include the constant of integration.

    8 x^4 + (5)x + C

    Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.

  2. 2. Find an indefinite integral of 12 x^3 + (7) with respect to x. Include the constant of integration.

    3 x^4 + (7)x + C

    Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.

  3. 3. Find an indefinite integral of 24 x^3 + (0) with respect to x. Include the constant of integration.

    6 x^4 + (0)x + C

    Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.

  4. 4. Find an indefinite integral of 6 x^2 + (-5) with respect to x. Include the constant of integration.

    2 x^3 + (-5)x + C

    Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.

  5. 5. Find an indefinite integral of 20 x^3 + (-2) with respect to x. Include the constant of integration.

    5 x^4 + (-2)x + C

    Power rule: ∫ x^n dx = x^(n+1)/(n+1) + C for n ≠ −1. Differentiate your answer to check.

WorksheetWise · en-au · 1/1

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Mathematics

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Secondary mathematics

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The accounting equation

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Practice assessments

Practice assessment · Secondary mathematics

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About these resources

WorksheetWise authors these practice questions and translations. Numerical answers are checked by automated tests. Reading and history include marking guidance. These materials have not been independently certified by an exam board.

For Australian classrooms and home learning. A4 paper is selected initially. Choose a short maths activity for revision or a tutoring session. Check year-level expectations with the school; these sheets are not certified against the Australian Curriculum.