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Simplify as much as possible. Again, 0 is the Heaviside step function. +∞ (a) Evaluate (b) Evaluate x=-8 [ð (a/3)] (x² +3x+2) sin(x)dr. (3) 0(x − 1)dx. - x0(x) 0(2-x)dx. x=0 +∞ (c) Evaluate (d) Find a distribution that equivalent to sin(ax) d'(x), but that involves neither

Simplify as much as possible. Again, 0 is the Heaviside step function. +∞ (a) Evaluate (b) Evaluate x=-8 [ð (a/3)] (x² +3x+2) sin(x)dr. (3) 0(x − 1)dx. - x0(x) 0(2-x)dx. x=0 +∞ (c) Evaluate (d) Find a distribution that equivalent to sin(ax) d'(x), but that involves neither

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do parts d-f please!

Simplify as much as possible. Again, 0 is the Heaviside step function. +00 (a) Evaluate x=-∞ 4 d -8(x/3) (x² +3x+2) sin(x)dx. [ [11/18 (1/3)] dx (b) Evaluate 8(3) 0(x − 1)dx. (c) Evaluate x=0 1+00 x=- -∞ x0(x) 0(2x)dx. (d) Find a distribution that is equivalent to sin(ax) d'(x), but that involves neither sin nor 8', when the distributions act on a test function (x). (e) Use the Heaviside and/or Dirac delta functions to find the volume mass density p(r) of a point mass m at the Cartesian coordinates (1,2,3). (f) Use the Heaviside and/or Dirac delta functions to find the volume charge density of an infinte line of charge parallel to the z-axis through the point (1,2,3) with constant linear charge density (i.e. charge per length) \.
Transcribed Image Text:Simplify as much as possible. Again, 0 is the Heaviside step function. +00 (a) Evaluate x=-∞ 4 d -8(x/3) (x² +3x+2) sin(x)dx. [ [11/18 (1/3)] dx (b) Evaluate 8(3) 0(x − 1)dx. (c) Evaluate x=0 1+00 x=- -∞ x0(x) 0(2x)dx. (d) Find a distribution that is equivalent to sin(ax) d'(x), but that involves neither sin nor 8', when the distributions act on a test function (x). (e) Use the Heaviside and/or Dirac delta functions to find the volume mass density p(r) of a point mass m at the Cartesian coordinates (1,2,3). (f) Use the Heaviside and/or Dirac delta functions to find the volume charge density of an infinte line of charge parallel to the z-axis through the point (1,2,3) with constant linear charge density (i.e. charge per length) \.
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