7.1, #6. f(x) = Öx, so
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F(x) = |
ó
õ
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Öx dx = (2/3)x3/2+C. |
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The condition F(0) = 0 holds if C = 0.
7.1, #8. f(x) = 5-(x6/6)-x7, so
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F(x) = |
ó
õ
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(5-(x6/6)-x7) dx = 5x-(x7/42)-(x8/8)+C. |
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The condition F(0) = 0 holds if C = 0.
7.1, #9. f(x) = sinx, so
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F(x) = |
ó
õ
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sinx dx = -cosx+C. |
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The condition F(0) = 0 holds if -1+C = 0, or equivalently, C = 1.
7.1, #12.
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ó
õ
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(x3/2+x-3/2) dx = (2x5/2/5)-2x-1/2+C |
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7.1, #14.
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ó
õ
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y2+1
y
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dy = |
ó
õ
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(y+y-1) dy = |
y2
2
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+ln|y|+C. |
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7.1, #16.
The derivative of ex is ex, but e1 = e, so to satisfy F(1) = 0 we need to take F(x) = ex-e.
File translated from TEX by TTH, version 2.00.
On 15 Aug 1999, 15:33.