MA1014_HW2_201012

# MA1014_HW2_201012 - Mathematics for Engineering Homework 2:...

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Mathematics for Engineering Homework 2: Sigma Notation and the Fundamental Theorem of Calculus fpm@itesm.mx 1. Find the following sum a) (3 i + 4) i = 1 100 2. Find the derivative of the following functions: a) F ( x ) = t t 3 + 2 dt 2 x 4 b) F ( x ) = 4 + 1 3 dt 0 x 2 c) F ( x ) = ( t 3 + 1) 10 dt 3 x x 3 d) F ( x ) = 4 + t 2 + 4 dt 1 x x 3. Find d dx 3 1 ( ) dt x 2 2 Λ Ν Μ Ξ Π Ο 1 4 dx 4. Find the average of the following functions in the given interval: a) f(x) = 2x - x 2 in the interval [0,2] b) f(x) = x 3 + 4x 2 - 3x + 2 in the interval [0,4] 5. Find the average of following functions in the given interval: a) f(x) = x 3 + x 2 in [0,3] b) f(x) = 5x 4 +4x 3 in [0,2] 6. Find the area between the function and the x -axis in the given interval: a) f(x) = 3x + 2 in the interval [0,5]

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## MA1014_HW2_201012 - Mathematics for Engineering Homework 2:...

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