Abstract In the paper, the authors 1.generalize Young’s integral inequality via Taylor’s theorems in terms of higher order derivatives and their norms, and2.apply newly-established integral inequalities to estimate several concrete definite integrals, including a definite integral of a function which plays an indispensable role in differential geometry and has a connection with the Lah numbers in combinatorics, the exponential integral, and the logarithmic integral.
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