1. ## Integral

Hi (Happy new year everyone!)

It is I = [-10,5] and Z = {-10, -8,-7,...,3, 4 ,5}

f integrable (furthermore f differentiable and continuous) at I = [-10,5]

It is f(-10)=f(-9)=...=f(3) = f(4) = f(5) = 0

Solve $\displaystyle \int^5_{-10} f(x) dx$

My question is: Is there any possibility to split the integral?

Because, what I know is (for example) $\displaystyle f = x^3 \ ; \ x \in I \ Z$

I this case I just have to solve

$\displaystyle \int_{-10}^9 x^3 dx +...+\int^5_4 x^3 dx$ ?

I find it kinda confusing because of f(a) = 0, if a element of Z

Rapha

2. Originally Posted by Rapha
Hi (Happy new year everyone!)

It is I = [-10,5] and Z = {-10, -8,-7,...,3, 4 ,5}

f integrable (furthermore f differentiable and continuous) at I = [-10,5]

It is f(-10)=f(-9)=...=f(3) = f(4) = f(5) = 0

Solve $\displaystyle \int^5_{-10} f(x) dx$
Up to this point you know nothing about $\displaystyle f$ other than it is zero on $\displaystyle Z$. If you apply a numerical integration method (say Simpson's rule) you will get:

$\displaystyle \int^5_{-10} f(x) dx\approx 0$

My question is: Is there any possibility to split the integral?

Because, what I know is (for example) $\displaystyle f = x^3 \ ; \ x \in I \ Z$

I this case I just have to solve

$\displaystyle \int_{-10}^9 x^3 dx +...+\int^5_4 x^3 dx$ ?

I find it kinda confusing because of f(a) = 0, if a element of Z

Rapha
Now the above seems to make no sense, what additional information do you have about $\displaystyle f$, and what are you trying to do?

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