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Find the points of intersection of the two curves.

Mathematics

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Step-by-step solution

2 steps

a) Find the area of the region lying between the curve y=4−x2y = 4 - x^2 and y=2x2−5y = 2x^2 - 5.

  1. Find the points of intersection of the two curves.

    Set the two equations equal to each other:

    4−x2=2x2−54 - x^2 = 2x^2 - 5 4+5=2x2+x24 + 5 = 2x^2 + x^2 9=3x29 = 3x^2 x2=3x^2 = 3 x=±3x = \pm \sqrt{3}

    The intersection points are x=−3x = -\sqrt{3} and x=3x = \sqrt{3}.

  2. Step 2

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