設(shè)函數(shù)f(x)連續(xù),F(xiàn)(x)=f(t)dt,試證:若f(x)是奇函數(shù),則F(x)是偶函數(shù).
設(shè)f(x)=dt,求f(x)+.
函數(shù)f(x),g(x)在(-∞,+∞)上連續(xù),且滿足等式f(x)=3x2+g(x)dx,g(x)=-x3+3x2f(x)dx.求f(x)和g(x).