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EDEXCEL A-Level Maths
Pure Maths Year 1
Chapter 13 - Intergration
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Created by
Sophia Lethbridge
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Cards (19)
What symbol represents the process of integration?
∫
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What does the equation ∫f′(x)dx = f(x) + c represent?
It represents the
indefinite integral
of f′(x)
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How is the process of integrating xⁿ expressed?
∫xⁿdx =
x
n
+
1
n
+
1
+
\frac{x^{n+1}}{n+1} +
n
+
1
x
n
+
1
+
c
c
c
,
n ≠ -1
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What does the dx in the integral signify?
It indicates integration with
respect
to x
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How do you integrate a polynomial function?
Integrate each term
one at a time
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What is the rule for integrating the sum of two functions?
∫
[f(x) + g(x)]
dx
= ∫f(x)dx + ∫g(x)dx
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What should you not do with the constant term c when integrating?
Do not
multiply
it by
k
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What is the result of integrating dy/dx = kxⁿ?
y =
k
n
+
1
x
n
+
1
+
\frac{k}{n+1}x^{n+1} +
n
+
1
k
x
n
+
1
+
c
c
c
, n ≠ -1
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How is the function notation expressed for f′(x) = kxⁿ?
f(x) =
k
n
+
1
x
n
+
1
+
\frac{k}{n+1}x^{n+1} +
n
+
1
k
x
n
+
1
+
c
c
c
, n ≠ -1
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Why can't you use the integration rule if n = -1?
Because
1/(n+1)
= 1/0 is
undefined
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What are the steps to find the constant of integration c?
Integrate
,
substitute
values,
solve for c
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What is a definite integral?
An integral calculated between two
limits
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What does a definite integral usually produce?
A
value
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What are the three stages of calculating a definite integral?
Write statement, integrate,
evaluate
f(b) - f(a)
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How can definite integration be used with areas under curves?
To
find
the
area
under
a
curve
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What is the formula for the area under a positive curve?
Area = ∫ᵇₐ y
dx
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What happens when the area bounded by a curve is below the x-axis?
∫ᵇₐ y
dx
gives a negative answer
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How can definite integration be combined with other geometric shapes?
To find
complicated
areas on graphs
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What are the key points summarized in Chapter 13?
If
dy/dx
= xⁿ, then y =
1
n
+
1
x
n
+
1
+
\frac{1}{n+1}x^{n+1} +
n
+
1
1
x
n
+
1
+
c
c
c
, n ≠ -1.
If dy/dx = kxⁿ, then y =
k
n
+
1
x
n
+
1
+
\frac{k}{n+1}x^{n+1} +
n
+
1
k
x
n
+
1
+
c
c
c
, n ≠ -1.
∫f′(x)dx = f(x) + c
∫[f(x) + g(x)]dx
= ∫f(x)dx + ∫g(x)dx
To find c: integrate, substitute values, solve.
Definite integral
: ∫ᵇₐf′(x)dx = f(b) - f(a).
Area
= ∫ᵇₐ y dx for positive curves.
Negative area for curves below x-axis.
Combine with
trapeziums
and triangles for complex areas.
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