Evaluate the definite integral from 1 to 2 e1x/x2dx

∫12e1xx2dxSubstitute 1x=uAnd −dxx2=duLimits of Integration will change from ∫12→∫1112=∫112=−∫12e1x(−dxx2)=−∫112euduRemember that∫abf(x)dx=−∫baf(x)dx−∫121eudu=[eu]121=e1−e12=e−eResult:∫12e1xx2dx=e−e

Expert answers to "Evaluate the definite integral from 1 to 2..."

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Calculus and Analysis
Integral Calculus
Integrals

hercegvm

Open question

2022-08-19

Evaluate the definite integral from 1 to 2

\frac{e^{1}}{x} / x^{2} d x

Answer & Explanation

Kristen Garrison

Beginner2022-08-20Added 11 answers

\int_{1}^{2} \frac{e^{\frac{1}{x}}}{x^{2}} d x

Substitute

\frac{1}{x} = u

And

- \frac{d x}{x^{2}} = d u

Limits of Integration will change from

\int_{1}^{2} \to \int_{\frac{1}{1}}^{\frac{1}{2}} = \int_{1}^{\frac{1}{2}}

= - \int_{1}^{2} e^{\frac{1}{x}} (- \frac{d x}{x^{2}})

= - \int_{1}^{\frac{1}{2}} e^{u} d u

Remember that

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x

- \int_{\frac{1}{2}}^{1} e^{u} d u = {[e^{u}]}_{\frac{1}{2}}^{1} = e^{1} - e^{\frac{1}{2}} = e - \sqrt{e}

Result:

\int_{1}^{2} \frac{e^{\frac{1}{x}}}{x^{2}} d x = e - \sqrt{e}

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