HW3 - ECE 302, Homework #3, Due 2/4...

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ECE 302, Homework #3, Due 2/4 http://www.ece.purdue.edu/ chihw/ECE302 09S.html Review of Calculus: Question 1: Compute the following integrals. Z 2 π 0 a cos( ωt + θ ) Z 2 π 0 a cos( ωt + θ ) da Question 2: Define a 2-D function f ( x,y ) as follows. f ( x,y ) = ( x/y 2 if y [1 , 2] and x [0 ,y ] 0 otherwise Compute the values of the following 2-dimensional integrals. Z 4 / 3 y =2 / 3 Z 3 / 2 x =1 / 2 f ( x,y ) dxdy Z 4 / 3 y =2 / 3 Z x = -∞ f ( x,y ) dxdy Z y = -∞ Z 3 / 2 x =1 / 2 f ( x,y ) dxdy. Question 3: Define a 1-D function f X ( x ) as follows. f X ( x ) = x if x [0 , 1] 1 2 if x (1 , 2] 0 otherwise Another function F ( x ) can be defined based on the integral of f X ( x ) as follows: F ( x ) = Z x s = -∞ f X ( s ) ds.
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1. Find the expression of F ( x ) for the case of x < 0. 2. Find the expression of F ( x ) for the case of x [0 , 1]. 3. Find the expression of F ( x ) for the case of x (1 , 2]. 4. Find the expression of F ( x ) for the case of x > 2. 5. Write down the complete expression of F ( x ) by considering the above four different cases. Your answer is simply a piecewise function that considers four different cases.
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HW3 - ECE 302, Homework #3, Due 2/4...

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