Calculus Methods
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| A xn | Differentiation: Move the index round to the front & reduce the index by 1. Leave any multiplicative constants in place --------------->
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nA xn-1 |
| (B/m) xm+1 | Integration:
Increase the index by 1, and divide any multiplicative constants
(including an implied 1 if there are no others) by the increased index. <---------------
| B xm |
| A sin(kx) A cos(kx) |
Differentiation:
Change sin() to cos() [or cos() to - sin()]. Pre-multiply by the
coefficient of x that is within the sin() or cos() function - but do
not tinker with the version of the cooefficient that is actually inside the sin or cos bracket. --------------->
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kA cos(kx) - kA sin(kx) |
| (B/k) sin(kx) - (B/k) cos(kx) |
Integration: Change cos() to sin() [or sin() to -cos()]. Divide by the coefficient of x
that is within the sin() or cos() function - but do not tinker with the
version of the cooefficient that is actually inside the sin or cos bracket.
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B cos(kx) B sin(kx) |
| A ekx | Differentiation: Pre-multiply
by
the coefficient of x that is in the exponent - but
do not tinker with the version of the cooefficient that is actually in
the exponent. Make no other changes, since the exponential function is
essentially its own differential coefficient.
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kA ekx |
| (B/k) ekx | Integration: Divide by
the coefficient of x that is in the exponent - but
do not tinker with the version of the cooefficient that is actually in
the exponent. Make no other changes, since the exponential function is
essentially its own integral.
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B ekx |
| A ln(kx) | Differentiation: Notice that the k vanishes. This is because ln(kx) may be split up as ln(k) + ln(x), the first term of which is a constant.
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A (1/x) |
| B ln(x) [ = ln(xB) ] |
Integration: This is a special case. Make sure that any coefficients of x are bundled up in B before carrying out the integration. You may or may not want to convert the answer to the form in [ ].
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B (1/x) |