Answered: "Evaluate the integrals ∫33dt3+t2"

Dillard

Answered question

2021-10-20

Evaluate the integrals

\int_{\sqrt{3}}^{3} \frac{d t}{3 + t^{2}}

Answer & Explanation

Alannej

Skilled2021-10-21Added 104 answers

We have to evaluate the integral

\int_{\sqrt{3}}^{3} \frac{d t}{3 + t^{2}}

We know

\int \frac{d x}{x^{2} + a^{2}} = \frac{1}{a} \tan^{- 1} (\frac{x}{a})

Therefore,

\int \frac{d x}{x^{2} + a^{2}} = \frac{1}{a} \tan^{- 1} (\frac{x}{a})

Therefore,

\int_{\sqrt{3}}^{3} = \int_{\sqrt{3}}^{3} \frac{d t}{t^{2} + {(\sqrt{3})}^{2}}

= [\frac{1}{\sqrt{3}} \tan^{- 1} {(\frac{t}{\sqrt{3}}]}_{\sqrt{3}}^{3}

= [\frac{1}{\sqrt{3}} \frac{π}{3} - \frac{1}{\sqrt{3}} \tan^{- 1} (1)]

= [\frac{1}{\sqrt{3}} (\frac{π}{3} - \frac{π}{4}]

= \frac{1}{\sqrt{3}} \frac{π}{12}

= \frac{π}{12 \sqrt{3}}

= \frac{\sqrt{3} π}{36}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?

Product

Company

Connect with us

Get Plainmath App

Google Play

Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus

Cyprus reg.number: ΗΕ 419361

E-mail us: support@plainmath.net

Our Service is useful for:

Plainmath is a platform aimed to help users to understand how to solve math problems by providing accumulated knowledge on different topics and accessible examples. Plainmath.net is owned and operated by RADIOPLUS EXPERTS LTD.