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Use the Midpoint Rule with Four Squares of Equal Size Rcos(x4+y4)dA,R={(x,y)0x0.4,0y0.4}\iint _ { R } \cos \left( x ^ { 4 } + y ^ { 4 } \right) d A , R = \{ ( x , y ) \mid 0 \leq x \leq 0.4,0 \leq y \leq 0.4 \}

question 47

Short Answer

Use the Midpoint Rule with four squares of equal size to estimate the double integral.
Rcos(x4+y4)dA,R={(x,y)0x0.4,0y0.4}\iint _ { R } \cos \left( x ^ { 4 } + y ^ { 4 } \right) d A , R = \{ ( x , y ) \mid 0 \leq x \leq 0.4,0 \leq y \leq 0.4 \}

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Definitions:

Alditol

A type of sugar alcohol formed by the reduction of the aldehyde or ketone group in monosaccharides.

L-Erythrose

A four-carbon sugar, or tetrose, with the chemical formula C4H8O4, one of the simplest aldose configurations.

NaBH4

Sodium borohydride, a reducing agent widely used in organic chemistry for the reduction of aldehydes, ketones, and aldehydes to alcohols.

Alditol

A type of sugar alcohol resulting from the hydrogenation of an aldose, used in food as a low-calorie sweetener.

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