# Exam-Style Question on Integration

## A mathematics exam-style question with a worked solution that can be revealed gradually

##### List Of QuestionsExam-Style QuestionMore Integration QuestionsMore on this Topic

Question id: 574. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is not allowed.

The function $$f$$ is defined by $$f(x) = 8 - 5 \sin{x}$$, for $$x \ge 0$$.

The diagram shows part of the graph of $$y = f (x)$$.

The shaded region is enclosed by the graph of $$y=f(x)$$ and the x-axis for the first three periods of the function.

(a) Find the exact value of the x-coordinate of the right side of the shaded region.

(b) Show that the area of the shaded region is $$48 \pi$$.

A hemisphere has a total surface area in square centimetres equal to the shaded area in the previous diagram.

(c) Find the radius of the hemisphere.

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