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calculus

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calculate the area bounded between the parabola y=x2, the straight line y=(x/2)+2, line x=1 and the y-axis.

  • calculus - ,

    make a sketch to see that in your region the straight line lies above the parabola.
    Find the intersection:
    x^2= x/2 + 2
    2x^2 - x - 4 = 0
    x = appr 1.686 or x = -1.183

    so we want:
    Area = [integral] (x/2 + 2 - x^2) dx from 0 to 1.686
    = (1/4)x^2 + 2x - (1/3)x^3 from 0 to 1.686
    = ...

    I will let you do the arithmetic.

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