What is the area of the region bounded by the curve $y = x^{2}$ and the line $y = 4$ ?

\frac{8}{3}

square unitsCorrect answerYour answer

\frac{16}{3}

square unitsCorrect answerYour answer

\frac{32}{3}

square unitsCorrect answerYour answer16 square unitsCorrect answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

They meet at $x = \pm 2$ ; the line lies above: $\int_{-2}^{2} (4 - x^{2})\,dx$ .
$16 - \frac{16}{3} = \frac{32}{3}$ square units.

Worth noting

$\frac{16}{3}$ is the area under the parabola from $-2$ to 2; the region is the part above it, inside the line.

Ten questions from Area of Bounded Regions, at your own pace.

Ten questions from Area of Bounded Regions, at your own pace.

What is the area of the region bounded by the curve y=x2y = x^{2}y=x2 and the line y=4y = 4y=4?