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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-za · 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-za · 1/1

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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 South African classrooms, tutors and families. A4 paper is selected initially. Choose practice by the skill being taught and use the separate answers for feedback. These sheets are not CAPS-certified. An Afrikaans edition is available through the language selector.