Evaluate ∫₀^√(3) x/(√(1 + x^2)) dx.

Definite Integrals & Area · Question 28 of 71

Question 28

MediumOriginal question

Evaluate $\int_0^{\sqrt{3}} \frac{x}{\sqrt{1 + x^2}}\,dx$ .

\frac{1}{2}

Correct answerYour answer

-1 + \sqrt{3}

Correct answerYour answer

1

Correct answerYour answer

2

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

$\frac{d}{dx}\sqrt{1 + x^2} = \frac{x}{\sqrt{1 + x^2}}$ , so an antiderivative is $\sqrt{1 + x^2}$ .
$\sqrt{4} - \sqrt{1} = 1$ .

Worth noting

2 is the antiderivative at the upper limit alone; $\sqrt{1} = 1$ must be subtracted.

Ten questions from Definite Integrals & Area, at your own pace.

Ten questions from Definite Integrals & Area, at your own pace.