Term
| Fundamental Theorem of Calculus |
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Definition
| int(f'(x)dx,x,a,b)=f(b)-f(a) |
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Term
| Second Fundamental Theorem of Calculus |
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Definition
| (d/dx)[int(f(t)dt,t,c,u)]=f(u)*u' |
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Term
| Average Value of f on [a,b] |
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Definition
| 1/(b-a)*int(f(x)dx,x,a,b) |
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Term
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Definition
=f(x)*(x-x)+f(x)*(x-x)+...
-rectangle length is always positive
-if rectangle is above x-axis, height is positive
-if height is below x-axis, height is negative |
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Term
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Definition
-Separate Variables
-Integrate
-Input coordinates
-Find C
-Find K (if necessary)
-Solve for y |
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Term
| Trapezoid Rule w/ equal subintervals |
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Definition
| =(b-a)/(2*n)*[f(x)+2*f(x)+2(x)+...+2*f(x)+f(x)] |
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Term
| Trapezoid Rule w/ unequal subintervals |
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Definition
| 1/(b-a)*[(f(x)+(f(x))/2*(x-x)+(f(x)+(f(x))/2*(x-x)+...] |
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Term
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Definition
Area=int(([top]-[bottom])dx,x,a,b)
Area=int(([right]-[left])dx,x,a,b) |
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Term
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Definition
Volume=π*int(([top]^(2)-[bottom]^(2))dx,x,a,b)
Volume=π*int(([right]^(2)-[left]^(2))dy,y,a,b) |
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Term
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Definition
Volume=int((area)dx,x,a,b)
Volume=int((area)dy,y,a,b) |
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