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

question 53

Essay

Use the Table of Integrals in your textbook to evaluate each of the following:
(a) $\int e ^ { x } \sec e ^ { x } d x$ (b) $\int \sin ^ { 4 } x \cos ^ { 2 } x d x$ (c) $\int \frac { 1 } { \cos ^ { 3 } x } d x$ (d) $\int x ^ { 3 } \sin x ^ { 2 } d x$ (e) $\int \frac { 1 } { \sqrt { 4 - 9 x ^ { 2 } } } d x$ (f) $\int _ { 0 } ^ { 2 } \frac { x ^ { 2 } } { \sqrt { 16 - x ^ { 2 } } } d x$ (g) $\int _ { 2 } ^ { 4 } \frac { d x } { \sqrt { 6 x - x ^ { 2 } - 5 } }$ (h) $\int _ { 0 } ^ { \pi / 2 } \frac { \sin t } { 1 + \cos ^ { 2 } t } d t$ (i) $\int _ { 2 } ^ { 5 } \frac { \sqrt { 4 + x ^ { 2 } } } { x ^ { 4 } } d x$ (j) $\int _ { 0 } ^ { x / 2 } e ^ { - x } \sin x d x$

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Definitions:

Total Profit

The overall financial gain made by a business after subtracting all costs from the total revenue generated from its operations.

AVC

Average Variable Cost; the total variable cost divided by the quantity of output produced.

ATC

Stands for "Average Total Cost," which refers to the total cost divided by the quantity of goods produced, in economics.

ATC Curve

Represents the average total cost of production at different levels of output, illustrating how cost per unit changes with changes in output.