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Pattern – 1 : Definite integration

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⋆ Pattern – 1

Definite integration never contains any arbitrary constant.

i.e. If $\int f\left(x\right)\ dx$ = F(x) + c, then

$\int_{a}^{b}f\left(x\right)\ dx$ = F(b) – F(a)

Proof :

Now, $\int_{a}^{b} f \left(x\right) dx$ = F(b) – F(a)

= [ F(b) + c ] – [ F(a) + c ]

= F(b) + c – F(a) – c

= F(b) – F(a)