Decide Whether Integration by Parts or Substitution Should Be Used $\int$

question 129

Multiple Choice

Decide whether integration by parts or substitution should be used to compute the indefinite integral $\int$ $\frac { - \mathrm { e } ^ { 1 / \mathrm { x } } } { \mathrm { x } ^ { 2 } }$ dx If substitution, indicate the value of u; if by parts, indicate f(x) and g(x) .

• A) substitution; u = \(x ^ { - 2 }\)
• B) integration by parts; f(x) =- \(\frac { 1 } { x ^ { 2 } }\) , g(x) = \(e ^ { 1 / x }\)
• C) integration by parts; f(x) = - \(e ^ { 1 / x }\) , g(x) = \(\frac { 1 } { x ^ { 2 } }\)
• D) substitution; u = \(\frac { 1 } { x }\)
• E) none of these
• Evaluate the integral.

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Definitions:

Independent Variable

In an experiment, the variable that is intentionally changed or manipulated to observe its effect on a dependent variable.

Statistically Significant

A term used to describe a result that is not likely to occur randomly, but rather is likely to be attributable to a specific cause.

Replicable

The ability of a study or experiment to be repeated with similar results, underscoring the reliability of the findings.

Statistically Significant

A measure of confidence in the results of a study or experiment that indicates the observed effects are unlikely to be due to chance.