Find the Value of the Integral $\int _ { 0 } ^ { x / 4 } \sin ^ { 2 } x \cos x d x$

question 46

Multiple Choice

Find the value of the integral $\int _ { 0 } ^ { x / 4 } \sin ^ { 2 } x \cos x d x$

• A) \(\frac { \sqrt { 2 } } { 18 }\)
• B) \(\frac { \pi } { 4 }\)
• C) \(\frac { 3 \pi } { 2 }\)
• D) \(\frac { \sqrt { 2 } } { 12 }\)
• E) \(\frac { \sqrt { 2 } } { 6 }\)
• F) \(\frac { \sqrt { 2 } } { 9 }\)
• G) \(\frac { 2 \pi } { 3 }\)
• H) \(\frac { \pi } { 2 }\)

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Definitions:

High Morals

The state of having strong ethical principles and adherence to good moral conduct.

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Fundamental truths or propositions that serve as the foundation for a system of belief, behavior, or reasoning.

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The process of justifying behaviors or decisions with logical, plausible reasons, often to conceal the true motives or feelings.

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Actions or practices that are morally wrong or violate societal norms or professional standards.