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Evaluate the definite integral.

$ \displaystyle \int^2_1 \frac{e^{1/x}}{x^2} \, dx $

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$$e-\sqrt{e}$$

01:19

Frank Lin

Calculus 1 / AB

Chapter 5

Integrals

Section 5

The Substitution Rule

Integration

Harvey Mudd College

University of Michigan - Ann Arbor

Boston College

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

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given our problem, we know that Are you convene? Seen as one of X which means our d axe once we take the derivative is negative Xcor d'you Which means now we know that we have negative times the intro from one to dio of either you do you now recall of the integral eat of the U is actually simply eat of the U and our upper bound is now going to be 1/2 because we know are a is gonna be 1/2 and r b is one over once or B is considered to be one So ensure that you remember to do the crypt bounds And now you consider attitude on we end up with even a square root of e.

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