Explanation Given: f ( x ) = x 3 , [ 0 , 3 ] Formula used: As according to fundamental theorem of calculus, ∫ a b f ( x ) d x = F ( b ) − F ( a ) Mean value theorem state that if f is continuous on the closed interval [ a , b ] then at c in interval [ a , b ] , ∫ a b f ( x ) d x = f ( c ) ( b − a ) Calculation: On considering the given function f ( x ) = x 3 . We will integrate the function f ( x ) in closed interval [ 0 , 3 ] to get, ∫ 0 3 f ( x ) d x = ∫ 0 3 x 3 d x = [ x 4 4 ] 0 3 As according to fundamental theorem of calculus ∫ a b f ( x ) d x = F ( b ) − F ( a ) The above integral is further solved as, ∫ 0 3 f ( x )

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Chapter 4.4, Problem 47E

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To calculate: The value of c by mean value theorem in f(x)=x3,[0,3].

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Chapter 4.4, Problem 46E

Chapter 4.4, Problem 48E

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The value of c by mean value theorem in f ( x ) = x 3 , [ 0 , 3 ] .

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To calculate: The value of c by mean value theorem in f(x)=x3,[0,3].

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