Express the limits as definite integral.

sagnuhh
2020-10-20
Answered

Express the limits as definite integral.

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Roosevelt Houghton

Answered 2020-10-21
Author has **106** answers

Step 1

Given

$\underset{\Vert p\to 0\Vert}{lim}\sum _{k=1}^{n}\left(\frac{1}{{c}_{k}}\right)\mathrm{\Delta}{x}_{k}$

Step 2

To express limits as a definite integrals.

The definition of definite integral is,

${\int}_{a}^{b}f\left(x\right)dx=\underset{n\to \mathrm{\infty}}{lim}\sum _{i=1}^{n}f\left({x}_{i}\right)\mathrm{\Delta}x$

Here$f\left({x}_{k}\right)=\frac{1}{{c}_{k}}$

And p is a partition of$[1,4]$ ,

Therefore,

$\underset{n\to \mathrm{\infty}}{lim}\sum _{k=1}^{n}\left(\frac{1}{{c}_{k}}\right)\mathrm{\Delta}{x}_{k}={\int}_{1}^{4}f\left(x\right)dx$

Given

Step 2

To express limits as a definite integrals.

The definition of definite integral is,

Here

And p is a partition of

Therefore,

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