Choosing the Right Technique (Calculus II)
Free printable university Calculus II worksheet: recognising which integration technique fits an integrand (u-substitution, parts and the tabular method, partial fractions, trig substitution), plus concept questions on LIATE and reference triangles.
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Calculus II · Math worksheet
Name
Date
Math
Integration Techniques: Choosing the Right Technique
For each integral, name the technique (u-substitution, integration by parts or the tabular method, partial fractions, or trigonometric substitution) and state the key choice: the u, the u and dv, the decomposition setup, or the substitution. Then answer the concept questions.
- 1.Which technique fits the integral of 2x dx, and what is the key choice?
- 2.Which technique fits the integral of dx, and what is the key choice?
- 3.Which technique fits the integral of (x + 1)/((x + 4)(x + 3)) dx, and what is the key setup?
- 4.Which technique fits the integral of dx/, and what is the key choice?
- 5.Which technique fits the integral of ln(x) dx, and what is the key choice?
- 6.Why is the tabular method valid, and when is it worth using instead of writing out integration by parts repeatedly?
- 7.Which trigonometric substitution goes with each form: , , ?
- 8.How can you CHECK any indefinite integration answer, whatever technique produced it?
- 9.Before applying partial fractions to a rational function, what TWO conditions must you check, and what do you do if either fails?
- 10.State the integration by parts formula, and say where it comes from.
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