Explanation Given Information: The flux of radio emission from the sun can be modeled by the function F ( t ) = 49.6 sin [ 0.602 ( t − 1.48 ) ] +111 where t is the number of years since January 1 , 1997 and F ( t ) is the flux of solar emissions of a specified wavelength at time t. Formula Used: The total change of the function from x = a to x = b is, ∫ a b f ( x ) d x . Where, function f ( x ) is the rate of change of quantity. The average of a function f ( x ) on an interval [ a , b ] is, f ¯ = 1 b − a ∫ a b f ( x ) d x . The sum and difference rules for an integral is, ∫ [ f ( x ) ± g ( x ) ] d x = ∫ f ( x ) d x ± ∫ g ( x ) d x Where, f ( x ) and g ( x ) are two functions. The formula for the integration of the function is, ∫ sin ( a x ) d x = − 1 a cos ( a x ) + C , where the function is f ( x ) = sin ( a x ) , and a and b are constants, with a ≠ 0 . Constant multiple rule is ∫ k ⋅ g ( x ) d x = k ∫ g ( x ) d x where k is a constant. Calculation: Consider the provided function, F ( t ) = 49.6 sin [ 0.602 ( t − 1.48 ) ] +111 . Here, F ( t ) is the flux of solar emissions since January 1 , 1997 for which t = 0 and for January 1 , 2001 , t = 4 . Determine the total flux of radio emission over the 5 year period from 4 to 9 using definite integral, F ( t ) = ∫ 4 9 ( 49.6 sin [ 0.602 ( t − 1.48 ) ] +111 ) d t Then determine the average of a function F ( t ) on an interval [ a , b ] by applying the formula f ¯ = 1 b − a ∫ a b f ( x ) d x . F ¯ = 1 9 − 4 ∫ 4 9 ( 49.6 sin [ 0.602 ( t − 1.48 ) ] +111 ) d t = 1 5 ∫ 4 9 ( 49.6 sin [ 0.602 ( t − 1.48 ) ] +111 ) d t To evaluate the integral 1 5 ∫ 4 9 ( 49.6 sin [ 0.602 ( t − 1.48 ) ] +111 ) d t , suppose that the function f ( u ) is ∫ 4 9 ( 49.6 sin [ 0.602 ( t − 1.48 ) ] ) d t and g ( u ) is ∫ 4 9 111 d t . Apply the sum rule, ∫ [ f ( u ) + g ( u ) ] d u = ∫ f ( u ) d u + ∫ g ( u ) d u 1 5 ∫ 4 9 ( 49

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ISBN: 8220103612005

Author: Costenoble

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Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 16.3, Problem 64E

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To calculate: The average flux of radio emission over the 5 year period beginning January 1, 2001.

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Chapter 16.3, Problem 63E

Chapter 16.3, Problem 65E

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The average flux of radio emission over the 5 year period beginning January 1 , 2001 .

Solution Summary: The author explains how the flux of radio emission from the sun can be modeled by the function f(t)=49.6mathrmsin

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To calculate: The average flux of radio emission over the 5 year period beginning January 1, 2001.

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