Find the Integral Using an Appropriate Trigonometric Substitution $$\int x \sqrt { 1 - x ^ { 2 } } d x$$

question 66

Short Answer

Find the integral using an appropriate trigonometric substitution.
$$\int x \sqrt { 1 - x ^ { 2 } } d x$$

---

Definitions:

Innocent Misrepresentation

A false statement made without malice or knowledge of its falsity, often leading to a misunderstanding in a contract or agreement.

Wagering Contract

An agreement between parties where the outcome is based on an uncertain event, in which one party stands to win or lose something of value.

Insurance Contract

A legally binding agreement between an insurer and the policyholder, specifying the claims which the insurer is legally required to pay in exchange for an initial payment, known as the premium.

Insurable Interest

A legitimate interest in ensuring the preservation or safety of an object or person, to the extent that loss or harm would result in financial loss or hardship.