Find the Integral Using an Appropriate Trigonometric Substitution $$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 36 } } d x$$

question 125

Multiple Choice

Find the integral using an appropriate trigonometric substitution.
$$\int \frac { x ^ { 3 } } { \sqrt { x ^ { 2 } + 36 } } d x$$

• A) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 36 \right) ^ { 3 / 2 } \sqrt { x ^ { 2 } + 36 } + C\)
• B) \(\frac { 1 } { 3 } \left( x ^ { 2 } + 72 \right) \sqrt { x ^ { 2 } + 36 } + C\)
• C) \(\frac { 1 } { 3 } \left( x ^ { 2 } - 72 \right) \sqrt { x ^ { 2 } + 36 } + C\)
• D) \(\frac { 1 } { 3 } \left( x ^ { 2 } - 36 \right) ^ { 3 / 2 } \sqrt { x ^ { 2 } + 36 } + C\)

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The habit of mentally assigning dollars to different accounts so that some dollars are worth more than others.

Overconfidence

The phenomenon where an individual's subjective confidence in their judgments is reliably greater than their objective accuracy.

Irrational Decisions

Choices made by individuals that contradict the best outcome from a rational point of view, often influenced by biases or lack of information.

Mental Accounting

The psychological process by which individuals classify, organize, and perceive their monetary resources and expenses.