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I want to count integral of $f(x)=x^2$ in range for example $0$ through $10$.

What should I read to do it by myself and apply it to other funcs ?

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First learn differential calculus, then integral calculus. The formula to be used here is :$\int_{a}^{b} x^{n} \ dx = \bigg[\displaystyle \frac{x^{n+1}}{n+1}\bigg]^{b}_{a}$

Note: the answer will be $\frac{b^{n+1}}{n+1} - \frac{a^{n+1}}{n+1}$

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    Note that it doesn't work for $x^{-1}$2013-03-26