# MAT - Paper 2016 - Q3

> Source: https://ollybritton.com/notes/maths/problems/mat/2016/q3/ · Updated: 2021-10-13 · Tags: mat, notes, maths

## Flashcards
### 2021-10-13
##### How could you write a general polynomial in sigma notation??
$$
\Sigma^d_{i = 0} c_i x^i
$$

##### How can you sometimes prove that something works for all polynomials??
Show that it works for individual terms and then consider how other terms can be added on.

##### What is the first fundamental theorem of calculus??
That you can differentiate an integral to retrieve the original function.

##### What is the second fundamental theorem of calculus, in terms of $f(x)$??
$$
\int^b_a f(x) \text{d}x = F(b) - F(a)
$$

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