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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-in · 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-in · 1/1

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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 English-medium practice in India. A4 paper is selected initially. Use short arithmetic sheets for revision and add your own lesson vocabulary to flashcards. These activities do not claim CBSE, ICSE or state-board alignment. A separate Hindi edition is available in the language selector.