# Exam-Style Question on Integration

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

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Question id: 446. This question is similar to one that appeared on an IB AI Standard paper (specimen) for 2021. The use of a calculator is allowed.

The following diagram shows part of the graph of:

$$f (x) = \frac{(9 + 4x) (6 - x)}{10}, x \in \mathbf R$$

The shaded region A is bounded by the x-axis, y-axis and the graph of $$f$$.

(a) Write down an integral for the area of region A.

(b) Find the area of region A.

The three points A (0 , 0) , B (6 , 9) and C (p , 0) define the vertices of a triangle.

Find the value of p, the x-coordinate of C , such that the area of the triangle is equal to the area of region A.

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