Question

Prove equation 1.41 from equation 1.40. Integration can be accomplished by making the following change of variable. Let e = kTx?, so that de = KT d(x2) and €112 = (kT)inx. Substitute these into equation 1.40 and inte- grate by parts, recalling that since d(uv) = u dv + v du, then Sd(uv) = Sudv + ſudu, so that ſudu = (uv) limits – Sudu, where the notation Ilimits indicates that the product (uu) should be evaluated at the limits used for the integrals.

Answer 1

The given integration im 1.40) is fCE - 13/2 2 T (Han) ve excelente ex de E Let E=KTR them de = KT d (2²) (KT)/2 x . Let a Let x = a When E=E fCE") = 27 In exp(-x) • KT+ d (2²) 1312 (KT) TIKT

2 xé 6727 + de e22 (T la e x2 2 Vi are a 2 5.10- & TH a 2. re lat N + ra erfe(a) Where exfc (a) TE 2 da e22

This is the expression in (1.41)