The Tabular Method (Repeated Parts) (Calculus II)
Free printable university Calculus II worksheet: repeated integration by parts organised as the tabular method, for polynomials times e^(ax), sin(ax) and cos(ax). Every answer key is computed and verified by differentiation.
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Calculus II · Math worksheet
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Date
Math
Integration Techniques: the Tabular Method (Repeated Parts)
Each integrand is a polynomial times e^(ax), sin(ax) or cos(ax), so integration by parts must be applied repeatedly. Use the tabular method: differentiate the polynomial down to zero in one column, integrate the other factor repeatedly in a second column, multiply diagonally with alternating signs and add. Include + C.
- 1.Use the tabular method (repeated integration by parts) to evaluate the integral of (-3x^2 - 3x + 1) dx.
- 2.Use the tabular method (repeated integration by parts) to evaluate the integral of (2x^3 - - 3x - 2) sin(x) dx.
- 3.Use the tabular method (repeated integration by parts) to evaluate the integral of (-3x^2 - 2x - 1) cos(x) dx.
- 4.Use the tabular method (repeated integration by parts) to evaluate the integral of (2x^3 - + 2x) dx.
- 5.Use the tabular method (repeated integration by parts) to evaluate the integral of (-2x^2 - 3x + 1) sin(x) dx.
- 6.Use the tabular method (repeated integration by parts) to evaluate the integral of (-2x^3 + 3x^2 + 1) cos(x) dx.
- 7.Use the tabular method (repeated integration by parts) to evaluate the integral of ( - 2x + 3) dx.
- 8.Use the tabular method (repeated integration by parts) to evaluate the integral of (3x^3 - 2x^2 + 3x + 3) sin(x) dx.
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