## Exam-Style Question on Integration## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 360. This question is similar to one that appeared on an IB Standard paper in 2018. The use of a calculator is allowed.

The following diagram shows the graph of \(f(x) = \cos(e^x) \; \text{for} \; 0 \le x \le 0.5\).

(a) Find the x-intercept of the graph of \(f(x)\).

The region enclosed by the graph of \(f(x)\), the y-axis and the x-axis is rotated 360° about the x-axis.

(b) Find the volume of the solid formed.

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