Use the Table of Integrals in Your Textbook to Evaluate $\int e ^ { 3 x } \cos 2 x d x$

question 201

Essay

Use the Table of Integrals in your textbook to evaluate each of the following:
(a) $\int e ^ { 3 x } \cos 2 x d x$ (b) $\int \sqrt { 4 x - x ^ { 2 } } d x$ (c) $\int \sqrt { 4 x - 25 x ^ { 2 } } d x$ (d) $\int u ^ { 3 } \sin u d u$ (e) $\int \cos ^ { 4 } ( 2 t ) d t$ (f) $\int \frac { 1 } { x ^ { 2 } + 2 x + 2 } d x$ (g) $\int \sqrt { 9 + 4 u ^ { 2 } } d u$ (h) $\int \sqrt { 9 - 4 u ^ { 2 } } d u$ (i) $\int \sqrt { 4 u ^ { 2 } - 9 } d u$ (j) $\int \sin ^ { 2 } t \cos t e ^ { \sin t } d t$

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Definitions:

Primacy Effect

The tendency to evaluate others in terms of first impressions.

Actor-Observer Effect

A psychological bias where people tend to attribute their own actions to situational factors while attributing others' actions to their personalities or character.

Fundamental Attribution Error

The tendency to overemphasize personality-based explanations for behaviors observed in others while underestimating the influence of external factors.

Social-Cognitive Perspective

A view in psychology that focuses on how people learn through observing others, and how they control their behavior through self-regulation and social interaction.