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Today's calculation of Integral 271

Source: 1989 Kanazawa University entrance exam

January 19, 2008

calculusintegrationfunctioncalculus computations

Problem Statement

For a positive constant number

a

, the function

f(x)

satisfies the following equation. f(x)\equal{}xe^{\minus{}\frac{x}{a}}\plus{}\frac{1}{a\plus{}1}\int_0^a f(t) dt (1) Express the value of

\int_0^a f(t)dt

in terms of

a.

(2) Find the maximum and minimum value of

f(x)

for \minus{}1\leq x\leq 1.