Flashcards
Integration
Cards in this deck (13)
- 1Essentially, what is integration?Reverse differentiation
- 2What is the constant of integration?Example: dy/dx=3x^2-1 , ∫3x^2-1 dx =
x^3-x+c.
C is the constant of integration - 3∫bx^m dx = .....bx^(m+1)/m+1 +c
(add 1 to power, divide by new power and add constant of integration, leave everything else the same) - 4Work out: ∫5x^9 dx5x^10/10 +c , same as 1/2x^10+c
- 5If we are given a derivative and also a coordinate, how do we find the value of c?Integrate normally, then sub in coordinates to the x and y values (y is f(x))
- 6Work out: ∫2x(x+3) dx through (1,5)f'(x)∫2x^2+6x dx
f(x)= 2x^3/3 + 6x^2/2 + c
5 = 2(1)^3/3 + 6(1)^2/2 + c
5 = 2/3 + 3 +c
c=4/3
f(x)= 2x^3/3 + 6x^2/2 + 4/3 - 7What do the number above and below ∫ mean? (e.g. 4∫0)Below = starts from
Above = ends at
(so 4∫0 starts from 0 and ends at 4) - 8Integrate 0∫-2 (4x^3+2x)dx[4x^4/4 + 2x^2/2 + c]^(0 -2) (integrate normally)
(4(0)^4/4 + 2(0)^2/2 + c) - (4(-2)^4/4 + 2(-2)^2/2 + c) = -20 (sub in 0 and -2 and subtract). 20 = non-direction area, and therefore answer. - 9How do you find the area under a curve using integration?Area = x∫y f(x) dx
- 10If he have a "negative area" and a "positive area" on the same graph what must we do to find the area?Integrate the areas separately and add them together
- 11If we have 2 functions on the same graph, how do we find the area using integration?We use a simultaneous equation to find x coordinate and then integrate normally
- 12How else can we find the area of a section of graph?Use formula for that specific shape along with worked out values
- 13Which side of the curve do we work out the area of?Under the curve
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- Integration
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