Set Up a Double Integral That Gives the Area of the Surface

question 24

Multiple Choice

Set up a double integral that gives the area of the surface on the graph of $f ( x , y ) = 10 \cos \left( x ^ { 2 } + y ^ { 2 } \right)$ over the region $R = \left\{ ( x , y ) : x ^ { 2 } + y ^ { 2 } \leq \frac { \pi } { 4 } \right\}$

• A)
• \(S = \int _ { - \sqrt { \pi / 4 } } ^ { \sqrt { \pi / 4 } } \sqrt { ( \pi / 4 ) - x ^ { 2 } } \sqrt { ( \pi / 4 ) - x ^ { 2 } } \sqrt { 1 + 400 \left( x ^ { 2 } + y ^ { 2 } \right) \sin ^ { 2 } \left( x ^ { 2 } + y ^ { 2 } \right) } d y d x\)
• B)
• \(S = \int _ { - \sqrt { \pi / 4 } } ^ { \sqrt { \pi / 4 } } \int _ { - \sqrt { ( \pi / 4 ) - x ^ { 2 } } } ^ { \sqrt { ( \pi / 4 ) - x ^ { 2 } } } \sqrt { 1 + 400 \left( x ^ { 2 } + y ^ { 2 } \right) \cos ^ { 2 } \left( x ^ { 2 } + y ^ { 2 } \right) } d y d x\)
• C)\(\begin{aligned} S = & \int _ { - \sqrt { ( \pi / 4 ) - y ^ { 2 } } } ^ { \sqrt { ( \pi / 4 ) - x ^ { 2 } } } \int ^ { 2 } - \sqrt { ( \pi / 4 ) - x ^ { 2 } } \sqrt { 3 + 400 \left( x ^ { 2 } + y ^ { 2 } \right) \cos ^ { 2 } \left( x ^ { 2 } + y ^ { 2 } \right) } d y d x \end{aligned}\)
• D)
• \(\begin{aligned} S = & \int _ { - \sqrt { ( \pi / 4 ) - y ^ { 2 } } - \sqrt { ( \pi / 4 ) - x ^ { 2 } } } ^ { \sqrt { ( \pi / 4 ) - y ^ { 2 } } } \sqrt { ( \pi / 4 ) - x ^ { 2 } } \end{aligned}\)
• E)
• \(S = \int _ { - \sqrt { ( \pi / 4 ) - y ^ { 2 } } - \sqrt { ( \pi / 4 ) - x ^ { 2 } } } ^ { \sqrt { ( \pi / 4 ) - y ^ { 2 } } \sqrt { ( \pi / 4 ) - x ^ { 2 } } } \sqrt { 1 + 400 \left( x ^ { 2 } + y ^ { 2 } \right) \cos ^ { 2 } \left( x ^ { 2 } + y ^ { 2 } \right) } d y d x\)

Analyze the process of breaking bad habits through structured steps.

Appreciate the importance of environmental conservation and individual contributions towards it.

Understand the impact of binge drinking on college students and recognize the role of peer pressure.

Recognize the societal impacts of high school dropouts.

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