math 1250 Worksheet 3 B part 1 of FToC.docx - Worksheet 3 B Part 1 of the Fundamental Theorem of Calculus x If x)=� f t dt where a is a constant then a

math 1250 Worksheet 3 B part 1 of FToC.docx - Worksheet 3 B...

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Worksheet 3 B - Part 1 of the Fundamental Theorem of Calculus: If ( x ) = a x f ( t ) dt , where a is a constant, then In each case find g' ( x ) : 1. g ( x ) = 3 x t ∙ sin ( t ) dt 2. g ( x ) = 3 x ( t 2 + 4 ) dt 3. g ( x ) = x 2 tan ( t ) dt 4. g ( x ) = x 5 t + ln ( t ) dt 5. g ( x ) = 2 x 3 t sin ( t ) dt 6. g ( x ) = 2 e x t 3 sin ( t ) dt 7. g ( x ) = 0 sin ( x ) ( t 3 + 4 t ) dt 8. g ( x ) = 0 ln ( x ) sin ( t 2 ) dt 9. g ( x ) = x 3 + x 2 2 t ∙ cos ( t ) dt
10. g ( x ) = 2 x 3 + 5 x 3 sin ( t 2 ) dt SOLUTIONS 1. g' ( x ) = x∙ sin ( x ) 2. g' ( x ) = x 2 + 4 3. g ' ( x ) =− tan ( x ) 4. g ' ( x ) =− ( x + ln ( x ) ) 5. g ' ( x ) = x 3 sin ( x 3 ) 3 x 2 = 3 x 5 sin ( x 3 ) 6. g ' ( x ) = ( e x ) 3 sin ( e x ) ∙e x = e 4 x sin ( e x ) 7. g' ( x ) = [ sin

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