Calculate the Iterated Integral $\int _ { 0 } ^ { \ln 2 } \left( \int _ { 1 } ^ { 2 } x y + y e ^ { x y } d x \right)$

question 78

Multiple Choice

Calculate the iterated integral $\int _ { 0 } ^ { \ln 2 } \left( \int _ { 1 } ^ { 2 } x y + y e ^ { x y } d x \right)$ dy.

• A) \(\frac { 3 } { 2 }\) ln - \(e ^ { 2 } \ln 2\) - \(\frac { 3 } { 2 }\)
• B) \(\frac { 3 } { 2 }\) ln 2 - \(\frac { 1 } { 2 }\) \(\mathrm{ex}^{2}\) - \(\frac { 5 } { 2 }\)
• C) \(\frac { 3 } { 4 }\) (ln 2) + \(\frac { 1 } { 2 }\)
• D) \(\frac { 3 } { 4 }\) \(( \ln 2 ) ^ { 2 }\) + \(\frac { 1 } { 2 }\)
• E) none of these

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Definitions:

Circular Reasoning

A logical fallacy in which the argument's conclusion is supported by premises that assume the conclusion's truth.

False Cause

A logical fallacy where a cause is incorrectly identified for an event or phenomenon, leading to incorrect conclusions.

Gambler's Fallacy

The erroneous belief that if a particular event occurs more frequently than normal during a past period, it is less likely to happen in the future (or vice versa).

Utilitarian

A philosophy or ethical theory that advocates for actions that maximize happiness and well-being for the majority.