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Q. 3

Expert-verifiedFound in: Page 384

Book edition
1st

Author(s)
Peter Kohn, Laura Taalman

Pages
1155 pages

ISBN
9781429241861

Without using absolute values, how many definite integrals would we need in order to calculate the absolute area between f(x) = sin x and the x-axis on $[-\frac{\mathrm{\pi}}{2},2\mathrm{\pi}]$ ?

Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?

three

positive

negative

The function is,

$f\left(x\right)=\mathrm{sin}x$

$\text{The objective is to determine the number of definite integrals would require in order to calculate}$

$\text{the absolute area between}f\left(x\right)=\mathrm{sin}x\text{and the}x\text{-axis on}\left[-\frac{\pi}{2},2\pi \right]\text{.}$

Consider, the following graph

$\text{From the above figure it is clear that}3\text{intervals are required.}$

The objective is to determine if the absolute area will be negative or positive.

The absolute area will be positive as the area covered will be positive.

$\text{The objective is to determine if the signed area will be positive or negative.}$

$\text{The signed area will be negative because the signed area on}[0,\pi ]\text{and}[\pi ,2\pi ]\text{are equal and}$

opposite.

$\text{Therefore, the answers are three, positive and negative}$

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