Integration is the inverse process of derivative. The real problem of Intergal calculus is, given the differential coefficient of a function, to discover the function itself.

Integral Formula :             $\int_{a}^{b} f(x) dx$

Here the sign $\int$ is called as Integral. The symbol dx indicates that the integration is to be performed with respect to the variable x.

The symbol $\int$ and dx, separately are meaningless. These 2 symbols may be regarded like a pair of brackets in which the function is to be integrated.

## Integration and Differentiation Formulas

This table gives the information of the Fundamental integral Formulas which follow immedietely from the standard differentiation formulas.

 No. Differentiation Integration 1. $\frac{\mathrm{d} }{\mathrm{d} x} (x^{n+1})=(n+1) x^{n}$ $\int x^{n} dx =\frac{x^{n+1}}{n+1} + c, n\neq -1$ 2. $\frac{\mathrm{d} }{\mathrm{d} x}(sin x) = cos x$ $\int cos x\ dx = sin x + c$ 3. $\frac{\mathrm{d} }{\mathrm{d} x}(cos x) = -sin x$ $\int sin x\ dx = -cos x + c$ 4. $\frac{\mathrm{d} }{\mathrm{d} x}(tan x) = sec^{2} x$ $\int sec^{2} x\ dx = tan x + c$

### Riemann Sum Calculator

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