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23 Cards in this Set
- Front
- Back
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d/dt(t^n) |
nt^n-1 |
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d/dt e^at |
ae^eat |
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d/dt(Sin at) |
aCosat |
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d/dt(Cosat) |
-aSinat |
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∫ t^n dt
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1/n+1 n^n+1 +c |
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∫ e^at dt
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1/a e^at +c |
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∫ Cosat dt
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1/a Sinat +c |
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∫ sinat dt
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-1/a Cosat +c |
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d/ dt Tant dt
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sec^2t |
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using the product rule |
y= uv then dy/dx = u'v + v'u |
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quotient rule |
if y= u/v then dy/dx= vu' - uv'/ v^2 |
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chain rule |
if y= f(u) then dy/dx= dy/du X du/dx |
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how to differentiate para metrically. |
(dy/dx) = (dy/dt)/(dt/dx) |
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how to differentiate a function where there are functions of x and why and it cannot be rearranged |
to differentiate when there are functions of and y that cannot be arranged differentiate dy/dx for the x values and differentiate the y value with respect to y and multiply by dy/dx
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how to integrate a function where there are individual functions on each side of the fraction. |
express as partial fractions then integrate, ln is likely to be used. |
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∫ x^n dx
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x^n+1/ n+1 |
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∫ 1/x dx
∫ 1/ax+b dx |
ln|x|+c 1/a ln|ax+b|+c |
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Integration by substitution |
1. select a value for u. 2. differentiate u to get du/dx 3. find dx/du by putting a 1 over the top. 4. rewrite function in terms of du and u 5. carry out the integration in terms of u 6. rewrite results in terms of x. ensure that if you are finding the definite integral that you us the correct values for u or x. |
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∫ f'(x)/f(x) dx |
ln|f(x)| +c |
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∫ uv' dx
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uv- ∫ vu' dx +c |
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∫ 1/ a^2 +x^2
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1/a tan^-1(x/a) +c |
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volume of revolution around x axis
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π ∫ y^2
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volume of revolution around y axis rearrange equation into terms of y |
π ∫ x^2
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