Solve the Problem $f ( x ) = \tan x$ Is Defined Over the Interval

question 1

Short Answer

Solve the problem.
- $f ( x ) = \tan x$ is defined over the interval $\left[ 0 , \frac { 3 } { 2 } \right]$
(a) Approximate the area A by partitioning $\left[ 0 , \frac { 3 } { 2 } \right]$ into 4 subintervals of equal length and choosing u as the left endpoint of each subinterval.
(b) Approximate the area A by partitioning $\left[ 0 , \frac { 3 } { 2 } \right]$ into 8 subintervals of equal length and choosing $\mathrm { u }$ as the right endpoint of each subinterval.
(c) Express the area A as an integral.
(d) Use a graphing utility to approximate this integral to three decimal places.

---

Definitions:

Unconventional Morality

A system of ethics that differs from the customary or established norms in a society.

Pleasing Others

The behavioral tendency to act in ways that are intended to gain approval or avoid disapproval from others.

Moral Equivalence

A concept suggesting that different actions, entities, or choices have the same moral or ethical value, often used in discussions of ethical dilemmas.

Nonviolence

A principle of resolving conflicts without the use of physical force, emphasizing peaceful means.