# $\int_{0}^{1}dx$

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!

• there is a 1 there in the integrand. Nov 5 '19 at 12:20

$$dx = 1.dx$$

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

$$hehe$$

• Correction, corrected. Should i delete my post? Nov 5 '19 at 12:52

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

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