do parts d-f please! Simplify as much as possible. Again, 0 is the Heaviside step function.+00(a) Evaluatex=-∞4d-8(x/3) (x² +3x+2) sin(x)dx.[ [11/18 (1/3)]dx(b) Evaluate 8(3) 0(x − 1)dx.(c) Evaluatex=01+00x=- -∞x0(x) 0(2x)dx.(d) Find a distribution that is equivalent to sin(ax) d'(x), but that involves neithersin 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 densityp(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 densityof an infinte line of charge parallel to the z-axis through the point (1,2,3) withconstant linear charge density (i.e. charge per length) \.

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Answered: Simplify as much as possible. Again, 0…

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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