f(x)=x³+∫(3,0)f(t)dt满足f(x)求∫(1,0)f(x)dx解
问题描述:
f(x)=x³+∫(3,0)f(t)dt满足f(x)求∫(1,0)f(x)dx解
答
两边取0到1的积分得:∫(1,0)f(x)dx=∫(1,0)x^3dx+∫(1,0)∫(3,0)f(t)dtdx即∫(1,0)f(x)dx=∫(1,0)x^3dx+∫(3,0)∫(1,0)f(t)dxdt=1/4+∫(3,0)f(t)dt原式两边去0到3的积分得:∫(3,0)f(x)dx=∫(3,0)x^3dx+∫(3,0)∫(3,0...