试用分部积分法证明：若f(x)连续，则
∫0x[∫0tf(x)dx]dt=∫x0f(t)(x-1)dt
证明：∫0x[∫0tf(x)dx]dt =t∫0tf(x)dx|0x-∫0xtd∫0xf(x)dx =x∫0xf(y)dy-∫0xtf(t)dt =∫0xf(t)dt-∫0xtf(t)dt =∫0xf(t)(x-t)dt
试用分部积分法证明：若f(x)连续，则
∫0x[∫0tf(x)dx]dt=∫x0f(t)(x-1)dt
证明：∫0x[∫0tf(x)dx]dt =t∫0tf(x)dx|0x-∫0xtd∫0xf(x)dx =x∫0xf(y)dy-∫0xtf(t)dt =∫0xf(t)dt-∫0xtf(t)dt =∫0xf(t)(x-t)dt
