Evaluate an improper integral involving an exponential function and a square root by using substitution and taking a limit.

Vault Of Euclid

Evaluating an Improper Integral with an Exponential Function

Integrals core

Evaluate \( \int_{1}^{\infty} \frac{e^{-\sqrt{x}}}{\sqrt{x}} \, dx \).

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Integration by substitution
Evaluating definite integrals
Limits at infinity
Properties of the exponential function

What this problem tests

Tests the ability to recognize when to use substitution, correctly change limits of integration, and evaluate limits at infinity for exponential functions.

This type of problem is standard in Calculus II courses when introducing improper integrals and reviewing integration techniques.

← today's set