Calculus check my answers

1. The general solution of the differential equation dy - 0.2x dx = 0 is a family of curves. These curves are all:
a. lines
b. hyperbolas
c. parabolas (my answer)
d. ellipses

2. The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of 2∫1 f(x) dx .
x 1 1.1 1.3 1.6 1.7 1.8 2.0
f(x) 1 3 5 8 10 11 14

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  1. dy/dx = 0.2
    constant slope is a parabola ???

    first trap = (1/2)(1+3)(1.1 - 1)
    second = (1/2)(3+5)(1.3 -1.1)
    etc

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  2. no, y' = 0.2x
    so, yes, a parabola.

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  3. whoops ! Go with Steve

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