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Expert-verified Found in: Page 384 ### Calculus

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 $\left[-\frac{\mathrm{\pi }}{2},2\mathrm{\pi }\right]$ ?Will the absolute area be positive or negative, and why? Will the signed area will be positive or negative, and why?

three

positive

negative

See the step by step solution

## Step1. Given Information

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

## Step2. Determining Area

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.

## Step3. Determining signed area

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

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

opposite.

$\text{Therefore, the answers are three, positive and negative}$ ### Want to see more solutions like these? 