# 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: 447. This question is similar to one that appeared on an A-Level paper (specimen) for 2017. The use of a calculator is allowed.

The diagram shows a sketch of the curve C with equation:

$$y=2x^{\frac32}-4x+3$$

The point P with coordinates (4, 3) lies on C.

The line L is the tangent to C at the point P.

The region A, shown shaded, is bounded by the curve C, the line L and the y-axis.

Find the area of A making your method clear.

Note that solutions based entirely on graphical or numerical methods are not acceptable.)

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