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  3. i need your help please with a clear explanation especially...

Question: i need your help please with a clear explanation especially...

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I NEED YOUR HELP PLEASE WITH A CLEAR EXPLANATION ESPECIALLY FOR B2 (a)z

My exams arenext week and I need to double check the andwers.

Clear explanation = Big like.
B3. (a) A sma mass m is given by the expression where ρ is the density and V is the volume. The air density at h mietres above the Earths surface is ρ(h) = 1.28 e-000124h kg/m3. Find the mass of a cylindrical column of air 4 metres in diameter and 25000 meters high from the Earths surface 10] (b) The length of an infinitesimal piece of arc is given by Find the are length of the curve given by , betweent1 and t-2 10] (e) Prove that Сdr 0 is convergent for values of n > 1. [Hint: Assume x 2 1]. [10)
B2. (a) Evaluate the following expressions 10) daco(2)ar dt d rln(t) r dr (b) Evaluate) dt, where H(t) is the Heaviside step function (c) Evaluate the double integral 1-( +2y2)drdy, where R is the region bounded by the line y and the curve y r (d) Evaluate tsin2(t2)6(t2-4)dt, where δ(t) is the Dirac delta function. [7] Please turn over
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