Use Various Trigonometric Identities to Simplify the Expression Then Integrate $$\int \sin ^ { 2 } \theta \cos 6 \theta d \theta$$

question 69

Multiple Choice

Use various trigonometric identities to simplify the expression then integrate.
- $$\int \sin ^ { 2 } \theta \cos 6 \theta d \theta$$

• A) \(\frac { 1 } { 12 } \sin 4 \theta - \frac { 1 } { 4 } \sin 6 \theta - \frac { 1 } { 32 } \sin 8 \theta + C\)
• B) \(\frac { 1 } { 12 } \sin 6 \theta - \frac { 1 } { 4 } \sin 4 \theta - \frac { 1 } { 32 } \sin 8 \theta + C\)
• C) \(\frac { 1 } { 12 } \sin 6 \theta - \frac { 1 } { 4 } \sin 8 \theta - \frac { 1 } { 32 } \sin 4 \theta + C\)
• D) \(\frac { 1 } { 2 } \sin 6 \theta - \frac { 1 } { 4 } \sin 4 \theta - \frac { 1 } { 8 } \sin 8 \theta + C\)

---

Definitions:

Stock Dividend

A dividend payment made to shareholders in the form of additional shares, rather than cash.

Net Income

The total earnings of a company after subtracting all expenses from revenue, including taxes and operating expenses.

Book Value

The net value of a company's assets minus its liabilities, often used to assess the company's worth.

Stock Dividend

A distribution of extra shares to shareholders, rather than distributing profits in cash.