Use a Double Integral to Find the Area of R $\int _ { y - 0 } ^ { y - 1 } \int _ { x - \frac { y } { 3 } } ^ { x - e ^ { y } } 1 d x d y = e - \frac { 7 } { 6 }$

question 7

Multiple Choice

Use a double integral to find the area of R. R is the region bounded by y = 3x,y = ln x,y = 0,and y = 1.

• A) \(\int _ { y - 0 } ^ { y - 1 } \int _ { x - \frac { y } { 3 } } ^ { x - e ^ { y } } 1 d x d y = e - \frac { 7 } { 6 }\)
• B) \(\int _ { y - 0 } ^ { y - 1 } \int _ { x - 0 } ^ { x - e ^ { y } } 1 d x d y = e - 1\)
• C) \(\int _ { x = 0 } ^ { x - e } \int _ { y - \ln x } ^ { y - 1 } 1 d y d x = e\)
• D) \(\int _ { x = 0 } ^ { x - 2 } \int _ { y - \operatorname { m } x } ^ { y - 3 x } 1 d y d x = \frac { 3 e ^ { 2 } } { 2 }\)

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Definitions:

Ratio

A mathematical ratio defining how often one number is included in or includes another.

Unknown Quantity

A variable or value within a mathematical problem or equation that has not yet been determined or identified.

Proportion

A constituent, allotment, or figure regarded in context with its aggregate.

Unknown Quantity

A variable or value in mathematics and algebra that is not known or specified.