Which integral gives the area of the smaller…

Which integral gives the area of the smaller part, to the right of x = 3?

Question 39

MediumOriginal question

The circle $x^{2} + y^{2} = 25$ is cut by the line $x = 3$ into a smaller and a larger part.

Which integral gives the area of the smaller part, to the right of $x = 3$ ?

\int_3^{5} \sqrt{25 - x^{2}}\,dx

Correct answerYour answer

2\int_0^{3} \sqrt{25 - x^{2}}\,dx

Correct answerYour answer

2\int_3^{5} (25 - x^{2})\,dx

Correct answerYour answer

2\int_3^{5} \sqrt{25 - x^{2}}\,dx

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer D

Correct answer: D

The part runs from $x = 3$ to $x = 5$ , and the circle is symmetric about the $x$ -axis.
Upper half $y = \sqrt{25 - x^{2}}$ , doubled: $2\int_3^{5} \sqrt{25 - x^{2}}\,dx$ .

Worth noting

Without the 2 the integral covers only the half above the $x$ -axis.

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

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