What is the total area between the line $y = x$ and the $x$ -axis from $x = -1$ to $x = 2$ ?

\frac{3}{2}

Correct answerYour answer

\frac{5}{2}

Correct answerYour answer

3

Correct answerYour answer

\frac{7}{2}

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer B

Correct answer: B

The line is below the axis on $[-1, 0]$ and above it on $[0, 2]$ : find each area separately.
$\left|\int_{-1}^{0} x\,dx\right| + \int_0^2 x\,dx = \frac{1}{2} + 2 = \frac{5}{2}$ .

Worth noting

$\frac{3}{2}$ is $\int_{-1}^{2} x\,dx$ , where the part below the axis cancels some of the rest.

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

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

What is the total area between the line y=xy = xy=x and the xxx-axis from x=−1x = -1x=−1 to x=2x = 2x=2?