## Definite Integral

Tool to calculate the integral of a function. The computation of an definite integral over an interval consist in measuring the area under the curve of the function to integrate.

## Results

Definite Integral -

Tag(s) : Mathematics

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# Definite Integral

## Primitive Calculator

This page deals with integral calculation on an interval. For the general case, see the calculation of primitives.

Also on dCode: Primitives Functions

## Definite Integral Calculator

Tool to calculate the integral of a function. The computation of an definite integral over an interval consist in measuring the area under the curve of the function to integrate.

### How to calculate a definite integral over an interval?

Enter the function, its lower and upper bounds and the variable to integrate, dCode will make the computation.

The integration calculation needs the compute the primitive function first.

### What is the list of common primitives?

FunctionPrimitive
$$\int \,\rm dx$$$$x + C$$
$$\int x^n\,\rm dx$$$$\frac{x^{n+1}}{n+1} + C \qquad n \ne -1$$
$$\int \frac{1}{x}\,\rm dx$$$$\ln \left| x \right| + C \qquad x \ne 0$$
$$\int \frac{1}{x-a} \, \rm dx$$$$\ln | x-a | + C \qquad x \ne a$$
$$\int \frac{1}{(x-a)^n} \, \rm dx$$$$-\frac{1}{(n-1)(x-a)^{n-1}} + C \qquad n \ne 1 , x \ne a$$
$$\int \frac{1}{1+x^2} \, \rm dx$$$$\operatorname{arctan}(x) + C$$
$$\int \frac{1}{a^2+x^2} \, \rm dx$$$$\frac{1}{a}\operatorname{arctan}{ \left( \frac{x}{a} \right) } + C \qquad a \ne 0$$
$$\int \frac{1}{1-x^2} \, \rm dx$$$$\frac{1}{2} \ln { \left| \frac{x+1}{x-1} \right| } + C$$
$$\int \ln (x)\,\rm dx$$$$x \ln (x) - x + C$$
$$\int \log_b (x)\,\rm dx$$$$x \log_b (x) - x \log_b (e) + C$$
$$\int e^x\,\rm dx$$$$e^x + C$$
$$\int a^x\,\rm dx$$$$\frac{a^x}{\ln (a)} + C \qquad a > 0 , a \ne 1$$
$$\int {1 \over \sqrt{1-x^2}} \, \rm dx$$$$\operatorname{arcsin} (x) + C$$
$$\int {-1 \over \sqrt{1-x^2}} \, \rm dx$$$$\operatorname{arccos} (x) + C$$
$$\int {x \over \sqrt{x^2-1}} \, \rm dx$$$$\sqrt{x^2-1} + C$$
$$\int \sin(x)\,\rm dx$$$$-\cos(x)+C$$
$$\int \cos(x)\,\rm dx$$$$\sin(x)+C$$
$$\int \tan(x)\,\rm dx$$$$-\ln|\cos(x)|+C$$