Area of region with line boundary

Questions finding the area of a region bounded by a polar curve, the initial line, and one or more half-lines θ=constant, often involving integration.

51 questions · Challenging +1.1

4.09c Area enclosed: by polar curve
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SPS SPS FM Pure 2025 February Q7
8 marks Challenging +1.3
The equation of a curve, in polar coordinates, is $$r = \sec \theta + \tan \theta, \quad \text{for } 0 \leq \theta \leq \frac{1}{4}\pi.$$
  1. Sketch the curve. [2]
  2. Find the exact area of the region bounded by the curve and the lines \(\theta = 0\) and \(\theta = \frac{1}{4}\pi\). [6]