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SS3: MATHEMATICS - 2ND TERM

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  1. Matrices I | Week 1
    6 Topics
  2. Matrices II | Week 2
    1 Topic
    |
    1 Quiz
  3. Commercial Arithmetic | Week 3
    7 Topics
    |
    1 Quiz
  4. Coordinate Geometry | Week 4
    8 Topics
    |
    1 Quiz
  5. Differentiation of Algebraic Expressions | Week 5 & 6
    7 Topics
  6. Application of Differentiation | Week 7
    4 Topics
    |
    1 Quiz
  7. Integration | Week 8
    8 Topics
    |
    1 Quiz



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When the variable x replaced by a linear expression in x, i.e. of the form ax + b such that we have (ax + b)n instead of xn , we evaluate the integral by  substitution.

Example:

Integrate (3x + 2)4

\(\scriptsize \int (3x + 2)^4dx, \;\\ \scriptsize let \; u = 3x +2 \)

\(\scriptsize \int u^4 dx\) we find x and substitute, \(\frac{du}{dx} \scriptsize = 3, \therefore dx =\normalsize \frac{du}{3} \)

\(\scriptsize \int u^4 \frac{du}{3} = \frac {1}{3}\int u^4 du = \frac {1}{3}\left( \frac{u^5}{5} \right) + c\)

Substituting u = 3x +2

= \(\frac {1}{3}\left( \frac{(3x + 2)^5}{5} \right) + c\)

= \( \frac{(3x + 2)^5}{15} + c\)

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