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I am really struggling on this $\int_{0}^{1}dx$.

Normally $\int_{0}^{1}xdx=\frac{x^2}{2}+c$ of the i need to replace the values of $x$ with the limit.

$\int_{0}^{1}dx$, because there is nothing inside the integrand I will asumed that is zero!

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    $\begingroup$ there is a 1 there in the integrand. $\endgroup$ Nov 5 '19 at 12:20
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$$ dx = 1.dx $$

$$ take \ a \ break, you're \ stressed $$

$$ hehe $$

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  • $\begingroup$ Correction, corrected. Should i delete my post? $\endgroup$ Nov 5 '19 at 12:52
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Normally $\int_{0}^{1}xdx=\frac{x^2}{2}+c$ of the i need to replace the values of $x$ with the limit.

By the power rule for integration

$$\int x^ndx=\frac{x^{n+1}}{n+1}+C $$

therefore

$$\int_0^1 x~dx=\left[\frac{x^2}{2}\right]_0^1=\frac{1}{2}$$

and

$$\int_0^1 dx=\int_0^1 1~dx=\int_0^1 x^0~dx=\left[\frac{x^1}{1}\right]_0^1=1$$

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