Questão de Matemática

K ƚĞŽƌĞŵĂ ĨƵŶĚĂŵĞŶƚĂů ĚŽ ĐĄůĐƵůŽ Ġ ƵŵĂ ƉŽĚĞƌŽƐĂ ĨĞƌƌĂŵĞŶƚĂ ƉĂƌĂ Ă DĂƚĞŵĄƟĐĂ͕ ƉŽŝƐ Ġ ĂŵƉůĂŵĞŶƚĞ ƵƟůŝnjĂĚŽĞŵƐƵĂƐĚŝǀĞƌƐĂƐƐƵďĄƌĞĂƐ͘ŽůŽŶŐŽĚĂŚŝƐƚſƌŝĂ͕ ĚŝǀĞƌƐĂƐǀĞƌƐƁĞƐĚĞƐƐĞƚĞŽƌĞŵĂĨŽƌĂŵĚĞŵŽŶƐƚƌĂĚĂƐ͘ &ĂnjĞŶĚŽƵƐŽůŝǀƌĞŵĞŶƚĞĚĞƐƐĂƐǀĞƌƐƁĞƐ͕ĐŽŶƐŝĚĞƌĂŶĚŽ ĚƵĂƐĨƵŶĕƁĞƐf, g : [a, b] o RĐŽŶơŶƵĂƐŶŽŝŶƚĞƌǀĂůŽ ĨĞĐŚĂĚŽĞůŝŵŝƚĂĚŽ[a, b]ĞĚĞĮŶŝŶĚŽF, G : [a, b]o RƉŽƌ x x F(x) = a + f(t)dt e G(x) = b + g(t)dt͕ a a ƉĂƌĂƚŽĚŽx  [a, b]͕ĂǀĂůŝĞĂƐƐĞŐƵŝŶƚĞƐĂƐƐĞƌĕƁĞƐĞĂ ƌĞůĂĕĆŽƉƌŽƉŽƐƚĂĞŶƚƌĞĞůĂƐ͘ WĂƌĂƚŽĚŽx  [a, b]͕ƚĞŵͲƐĞƋƵĞ x F(x) G(x) - F(a)G(a) = [f(t)G(t) + F(t)g(t)]dt] a PORQUE ^Ğ<͗ [a, b] oRƉŽƐƐƵŝĚĞƌŝǀĂĚĂŝŶƚĞŐƌĄǀĞů͕ĞŶƚĆŽ b d <(b) <(a) = <(t)dt. a dt ĐĞƌĐĂĚĞƐƐĂƐĂƐƐĞƌĕƁĞƐ͕ĂƐƐŝŶĂůĞĂĂůƚĞƌŶĂƟǀĂĐŽƌƌĞƚĂ͘