Let be a positive constant

MATHEMATICS · Multi-part · AP · Calculus BC · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Let aa be a positive constant. Evaluate the improper integral L(a)=∫0∞e−ax dxL(a)=\displaystyle \int_{0}^{\infty} e^{-ax}\,dx. (a) Verify directly from the definition of an improper integral that L(a)L(a) converges for all a>0a>0. (b) Calculate L(a)L(a) as an explicit function of aa.

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