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Pattern – 7 : Definite integration

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Pattern – 7 :

\int_{a}^{a}f\left(x\right)dx=0

Proof :

Let ∫f(x) dx = F(x) + c

Now,

\int_{a}^{a}f\left(x\right)dx=\ \left[F\left(x\right)\right]_a^a

= F(a) – F(a)

= 0

 

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