TBIL-Calc Integration strategy (TI7)

Section 5.7 Integration strategy (TI7)

Learning Outcomes

I can select appropriate strategies for integration.

Activity 5.7.1.

Consider the integral $\int e^{t} \tan (e^{t}) \sec^{2} (e^{t}) d t .$ Which strategy is a reasonable first step to make progress towards evaluating this integral?

The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions

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Activity 5.7.2.

Consider the integral $\int \frac{2 x + 3}{1 + x^{2}} d x .$ Which strategy is a reasonable first step to make progress towards evaluating this integral?

The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions

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Activity 5.7.3.

Consider the integral $\int \frac{x}{\sqrt[3]{1 - x^{2}}} d x .$ Which strategy is a reasonable first step to make progress towards evaluating this integral?

The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions

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Activity 5.7.4.

Consider the integral $\int \frac{1}{2 x \sqrt{1 - 36 x^{2}}} d x .$ Which strategy is a reasonable first step to make progress towards evaluating this integral?

The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions

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Activity 5.7.5.

Consider the integral $\int t^{5} \cos (t^{3}) d t .$ Which strategy is a reasonable first step to make progress towards evaluating this integral?

The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions

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Activity 5.7.6.

Consider the integral $\int \frac{1}{1 + e^{x}} d x .$ Which strategy is a reasonable first step to make progress towards evaluating this integral?

The method of substitution
The method of integration by parts
Trigonometric substitution
Using a table of integrals
The method of partial fractions

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Subsection 5.7.1 Videos

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Figure 81. Video: I can select appropriate strategies for integration