DejarP ser una partición de[a,b] y definir\ [\ begin {eqnarray*} m_j\ ar=\ sup\ set {f (x)} {x_ {j-1}\ le x\ le x_j},\\ m_j\ ar= \ inf\ set {f (x)} {x_ {j-1}\ le x\ le x_j},\ \ overline {M} _j...DejarP ser una partición de[a,b] y definir\ [\ begin {eqnarray*} m_j\ ar=\ sup\ set {f (x)} {x_ {j-1}\ le x\ le x_j},\\ m_j\ ar= \ inf\ set {f (x)} {x_ {j-1}\ le x\ le x_j},\ \ overline {M} _j\ ar=\ sup\ set {|f (x) |} {x_ {j-1}\ le x\ le x_j},\\ \ overline {m} _j\ ar=\ inf\ set {|f (x) |} {x_ {j-1}\ le x\ le x_j}. \ end {eqnarray*}\] Entonces\ [\ begin {ecuación}\ label {eq:3.3.4} \ begin {array} {rcl} \ overline {M} _j-\ overline {m} _j\ ar= \ dst\ sup\ set {|f (x) |-|f (x') |} {x_ {j…
