Evaluate the Definite Integral of the Algebraic Function $\int _ { 7 } ^ { 10 } \left( s ^ { \frac { 7 } { 4 } } + s ^ { \frac { 4 } { 7 } } \right) d s$

question 55

Multiple Choice

Evaluate the definite integral of the algebraic function.
$\int _ { 7 } ^ { 10 } \left( s ^ { \frac { 7 } { 4 } } + s ^ { \frac { 4 } { 7 } } \right) d s$ Use a graphing utility to verify your results.

• A)\(\frac { 400 ( 10 ) ^ { \frac { 3 } { 4 } } - 196 ( 7 ) ^ { \frac { 3 } { 4 } } + 70 ( 10 ) ^ { \frac { 4 } { 7 } } - 49 ( 7 ) ^ { \frac { 4 } { 7 } } } { 28 }\)
• B)\(\frac { 400 ( 10 ) ^ { \frac { 3 } { 4 } } - 196 ( 7 ) ^ { \frac { 3 } { 4 } } + 70 ( 10 ) ^ { \frac { 4 } { 7 } } - 49 ( 7 ) ^ { \frac { 4 } { 7 } } } { 11 }\)
• C)\(\frac { 400 ( 10 ) ^ { \frac { 3 } { 4 } } + 196 ( 7 ) ^ { \frac { 3 } { 4 } } + 70 ( 10 ) ^ { \frac { 4 } { 7 } } + 49 ( 7 ) ^ { \frac { 4 } { 7 } } } { 11 }\)
• D)\(\frac { - 400 ( 10 ) ^ { \frac { 3 } { 4 } } + 196 ( 7 ) ^ { \frac { 3 } { 4 } } - 70 ( 10 ) ^ { \frac { 4 } { 7 } } + 49 ( 7 ) ^ { \frac { 4 } { 7 } } } { 11 }\)
• E)\(\frac { - 400 ( 10 ) ^ { \frac { 3 } { 4 } } + 196 ( 7 ) ^ { \frac { 3 } { 4 } } - 70 ( 10 ) ^ { \frac { 4 } { 7 } } + 49 ( 7 ) ^ { \frac { 4 } { 7 } } } { 28 }\)

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Definitions:

Density

A measure of mass per unit volume of a substance, influencing how materials interact, such as floating or sinking in water.

Slab Pull

A mechanism that contributes to plate tectonics, involving the subduction of oceanic plates pulling the trailing lithosphere into subduction zones.

Asthenosphere

The upper mantle's region directly beneath the lithosphere, characterized by high viscosity, mechanical weakness, and ductile deformation.

Oceanic Lithosphere

The rigid outer layer of the Earth under the ocean basins, composed of the crust and upper mantle that is specifically associated with oceanic regions.