Question

evaluate integral 0 to 1 Mod X by x dx​

Answer 1

Answer:

Please see the attachment

Answer 2

Concept

In mathematics, an integral is a numerical number equal to the area under the graph of a function for some interval (definite integral) or a new function whose derivative is the original function (indefinite integral) (indefinite integral).

Given

The given integral is $\int\limits^1_0 {\frac{|x|}{x}} dx$.

Find

We have to evaluate the given integral.

Solution

Let us assume $I=\int\limits^1_0 {\frac{|x|}{x}} dx$.

Here, we take $\left(|x|=\left\{\begin{array}{ll}x, &\text{ if } x\geq 0\\ -x, &\text{ if } x < 0\end{array}\right.\right)$.

So, we write the given integral as

$I=\int_{0}^1 \frac{x}{x}dx$

$\Rightarrow I=\int_{0}^1 1dx$

Now, we will do the integration.

$I=x\left|_{0}^1$

$\Rightarrow x=1$

Hence, the integral of $I=\int\limits^1_0 {\frac{|x|}{x}} dx$ is $I=1$.

#SPJ2