Explanation Given: The function, F ( t ) = ∫ 2 x ( t 3 + 2 t − 2 ) d t . Formula used: The integration of type x n are solved as f ( x ) = ∫ x n d x = x n + 1 n + 1 Calculation: The function F ( v ) can be made into F ( x ) by solving the integral as shown below. ∫ 2 x ( t 3 + 2 t − 2 ) d t = ∫ 2 x t 3 d t + 2 ∫ 2 x t d t − 2 ∫ 2 x d t = [ t 4 4 ] 2 x + 2 [ t 2 2 ] 2 x − 2 [ t ] 2 x = x 4 − ( 2 ) 4 4 + x 2 − 4 − 2 ( x − 2 ) = x 4 4 − 4 + x 2 − 4 − 2 x + 4 On further calculation, F ( x ) = x 4 4 + x 2 − 2 x − 4 On substituting by x = 2 to calculate F ( 2 )

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Chapter 4.4, Problem 64E

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To calculate: The function F in terms of x and find value of function F(t)=∫2x(t3+2t−2)dt at x=2,5,8.

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Chapter 4.4, Problem 63E

Chapter 4.4, Problem 65E

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The function F in terms of x and find value of function F ( t ) = ∫ 2 x ( t 3 + 2 t − 2 ) d t at x = 2 , 5 , 8 .

Solution Summary: The author explains how the function F can be made into F(x) by solving the integral.

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To calculate: The function F in terms of x and find value of function F(t)=∫2x(t3+2t−2)dt at x=2,5,8.

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