1.Suppose that f is a conti function which satisfies the intergral equation
x f(t)
f(x)=2 + S ------------ dt, x>=0 then f(1)=?
0 (t+2)(t+3)
-x^2(t^2+1)
x -t^2 2 1 e
2.If f(x)={S e dt} , g(x)=S ------------- dt, then
0 0 2
t +1
(1) Show that g'(x)+f'(x)=0 for all of x
(2) Use (1) to show that g(x)+f(x)=π/4
∞ -t^2 dt
(3) Use (2) to prove that S e = √π/2
0
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