The shaded region is enclosed by the curve    and the line  , as shown in the diagram. The line    meets the curve    at    and  . Do NOT prove this.
 

1.  Use integration to find the area of the shaded region.  (2 marks)
   

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2. Use the Trapezoidal rule and four function values to approximate the area of the shaded region.  (2 marks)
   

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The point is chosen on the curve    so that the tangent at is parallel to the line    and the -coordinate of is positive

3.  Show that the coordinates of are  .  (2 marks)
   

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4.  Using the perpendicular distance formula  ,  find the area of  .  (2 marks)
   

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