Question 1

Paper 1Medium6 marks

Figure 1 shows the graph of y=4xsin⁡(x2)y=4x\sin(x^2) for 0≤x≤π0\leq x\leq\sqrt{\pi} Angles are measured in radians. The shaded region is bounded by the curve and the xx-axis.

00.511.5√π20123456xy
(a)

Write down the upper limit represented by the shaded region.

[1]
(b)

Find ∫4xsin⁡(x2) dx\displaystyle\int 4x\sin(x^2)\,dx

[2]
(c)

Hence find the exact xx-coordinate that divides the shaded region into two equal areas.

[3]

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