Evaluate ∫₀^π/2 x cos x dx.

Definite Integrals & Area · Question 31 of 71

Question 31

HardOriginal question

Evaluate $\int_{0}^{\frac{\pi}{2}} x \cos x\,dx$ .

1 - \frac{\pi}{2}

Correct answerYour answer

-1 + \frac{\pi}{2}

Correct answerYour answer

-2 + \pi

Correct answerYour answer

\frac{\pi}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

An antiderivative is $F(x) = x \sin x + \cos x$ .
By the fundamental theorem, the integral is $F(\frac{\pi}{2}) - F(0) = -1 + \frac{\pi}{2}$ .

Worth noting

$\frac{\pi}{2}$ is $F(\frac{\pi}{2})$ alone: $F(0)$ was not subtracted.

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

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