Question

3- Solve the following improper integrals 1="e 'dt 4- Solve the following improper integrals I

Answer 1

3

footvtedt = 3V5 – 3V 7 ert(0) Steps SotVie hdt Hide Steps Compute the indefinite integral: ſt tedt= -e StVtedt Hide Steps t/te-xe- Wiet =b+c-O- Apply exponent rule: a tvte- te-1

Show Steps Apply Integration By Parts: u=ti,v=e-t =-*-5--Vedt Hide Steps s-le-Vid=-(-2"Vi + verf ( 17 )) s - e *Vedt Take the constant out: fa-f(x) dx =a 5t(x) dx = - se "Vedt Show Steps Apply Integration By Parts: u=vt,v're =-(-V7-5 Seda - olva) Hide Steps Take the constant out: Ja-f(x) dx = a Sf(x) dx

Apply u-substitution: u=vt Show Steps = S2e=u'au Take the constant out: Sa-f(x) dx = a - Sf(x) == 2.5e-up du Use the nonelementary integral: Se-u? du= vert () = 2. verf(u) Substitute back u=vt = 2. verf(VI) Hide Steps Simplify = z; 2. Va cr(VT): - va ertv7) . 2. Vert(VE)

Multiply fractions: abd =2.0. се се = -1,2V erf(17) Cancel the common factor: 2 = -erf(V7 )?. Ya Multiply: 1.VTOVT =-Verf(VT) = - V ert(v7) =-(-21-1- va qol v7))) Simplify =-(-2Ve + Verl v7) =-441-(- (-1*Ve + va erk v7)))

Simplify =-*+}(-e+Ve + van art(v7)) Add a constant to the solution 6 =-+*+(-e've + sa ( V7 )) +c Compute the boundaries: SootVie-*a = 317 3v. erf() = 3V7. – 377 or(0) Simplify = 3V1 – 3V erf(0)

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