Question

Integrate 1/x dx with limits 2-4

Answer 1

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Answer 2

Integration is one of the most important concepts in calculus. Applications of integrals include finding the area under the curve, finding the values of various parameters and quantities in subjects of engineering and science. Let's solve an example related to integrals.

We know that,

$d/dx[ ln(x)] =1 / x$

Thus, we will do the counter process here to find the integral of $1/x$

Hence, the integral of $1/x$ is given by the loge|x| which is the natural logarithm of absolute x also represented as or ln x.

Note: We can't use the integral identity for xn here, since ∫xn dx = xn + $1/(n + 1) + C$, and here, for $1/x$, we have n = -1. Hence, ∫x-1 dx = x0/0 = undefined.

Also, we add a constant C to it if it's an indefinite integral.

$\int\limits^x_2 \frac{1}{x} \, dx =[ln{x}]^4_2$

$=ln(4)-ln(2)$

$=2ln(2)-ln(2)$

$=ln2$

$\frac{ln(ax+b)}{a}$

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