Question

(a) Use the obvious identity i-re-u to evaluate the integral sin dr. (b) Use the double angle formula and integrate by parts to evaluate the integral in da (c) Prove that both of these integrals converge as improper Riemann integrals (albeit for different reasons). (d) Use scaling to evaluate the integral r.sinatz dr dar for tE R.

Answer 1

SOLUTION

$\int_{-\infty}^{+\infty}\frac{sinx}{x}=\pi$

EXPLANATION

We known Sa Sa C) Ps itsGymmahy abod W Can ytis euen undtion 0 Uing this, ue lead a to 4his mex compudathe fom -2t We rt

since dr 6 Now, at fst slove, "fの sme de -X tit i t+ 2 an() 2.