$\text { Find } \int \sin 5 x \cos 10 x d x \text {. }$

question 89

Multiple Choice

$\text { Find } \int \sin 5 x \cos 10 x d x \text {. }$

• A) \(\int \sin 5 x \cos 10 x d x = \frac { 1 } { 30 } ( 3 \cos 5 x - \cos 15 x ) + C\)
• B) \(\int \sin 5 x \cos 10 x d x = \frac { 1 } { 15 } ( 3 \cos 14 x + 3 \cos 5 x ) + C\)
• C) \(\int \sin 5 x \cos 10 x d x = \frac { 1 } { 31 } ( \cos 15 x - 3 \cos 5 x ) + C\)
• D) \(\int \sin 5 x \cos 10 x d x = \frac { 1 } { 30 } ( 4 \cos 5 x + \cos 14 x ) + C\)
• E) \(\int \sin 5 x \cos 10 x d x = \frac { 1 } { 31 } ( 3 \cos 5 x - \cos 15 x ) + C\)

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Definitions:

Monopolistically Competitive

Refers to a market structure where many firms sell products that are similar but not identical, allowing for some degree of market power.

Purely Competitive

A market scenario where the selling price of products is determined by the overall supply and demand, with numerous sellers and homogeneous products.

Elastic

Describes a condition in economics where the demand or supply for a product is sensitive to changes in price, leading to significant changes in quantity demanded or supplied.

Herfindahl Index

A measure of market concentration, determining the competitiveness of an industry based on the sum of the squares of the market shares of all firms within it.