f:[0,1]->R is continuous and nonconstant function. F is the indefinite integral of f such that F(0)=F(1)=0. m and M are the minimum and the maximum values of f.Now we define g:[0,1]->R , g(x)=xf(x) and the indefinite integral of g,G, such that G(0)=0. How can you prove that $|G(1)|<=-mM/(2(M-m))$ ?
2026-03-27 21:34:50.1774647290
Inequality with indefinite integrals and extreme points
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