Integrate in mathematica

The Wolfram Language contains a very powerful system of integration.

IntegrateChangeVariables [ integral , u , trans ]. Apply the change of variables to an indefinite integral:. Apply the change of variables to a definite integral:. Compare the result with the original approximation of the multiple integral:. The transformation can be given with the old variables in terms of the new ones, :.

Integrate in mathematica

Integrate [ f , x ]. Use to enter the lower limit, then for the upper limit:. Use intt to enter a template and to move between fields:. Use dintt to enter a template and to move between fields:. Multiple integral with x integration last:. Enter a region specification in an underscript using :. Use rintt to enter a template and to move between fields:. Invoke NIntegrate automatically if symbolic integration fails:. Sometimes they involve sums of Root objects:. Integrate returns antiderivatives valid in the complex plane where applicable:. A common antiderivative found in integral tables for is :. This is a valid antiderivative for real values of :. But the imaginary parts differ by on any interval where is negative:.

Use the Inactive form of Integrate :.

Wolfram Alpha is a great tool for calculating antiderivatives and definite integrals, double and triple integrals, and improper integrals. The Wolfram Alpha Integral Calculator also shows plots, alternate forms and other relevant information to enhance your mathematical intuition. Use Math Input above or enter your integral calculator queries using plain English. To avoid ambiguous queries, make sure to use parentheses where necessary. Here are some examples illustrating how to ask for an integral using plain English. Get immediate feedback and guidance with step-by-step solutions for integrals and Wolfram Problem Generator. The indefinite integral of , denoted , is defined to be the antiderivative of.

Integrate [ f , x ]. Use to enter the lower limit, then for the upper limit:. Use intt to enter a template and to move between fields:. Use dintt to enter a template and to move between fields:. Multiple integral with x integration last:. Enter a region specification in an underscript using :. Use rintt to enter a template and to move between fields:. Invoke NIntegrate automatically if symbolic integration fails:. Sometimes they involve sums of Root objects:. Integrate returns antiderivatives valid in the complex plane where applicable:.

Integrate in mathematica

The Wolfram Language function NIntegrate is a general numerical integrator. It can handle a wide range of one-dimensional and multidimensional integrals. Finding a numerical integral of a function over a region. In general, NIntegrate estimates the integral through sampling of the integrand value over the integration region. The various numerical integration methods prescribe the initial sampling steps and how the sampling evolves. NIntegrate uses algorithms called "integration strategies" that attempt to compute integral estimates that satisfy user-specified precision or accuracy goals.

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Enter a region specification in an underscript using :. Given a mass density , find the mass of region given by the following:. Reply to this discussion in reply to. The integral of a piecewise-constant function is the sum of the signed areas of the rectangles defined by its plot:. Define the region as an ImplicitRegion and integrate directly over the region:. The curve forms an infinity figure, traversed from red to purple as shown in the following plot:. Area Between Curves 7 Compute the area under the curve of from to :. The relevant parameter range is to :. Wolfram Language. IntegrateChangeVariables can be used to perform a change of variables for indefinite integrals, definite integrals, multiple integrals and integrals over geometric regions. The circulation of the vector field can be computed using Curl :. Suppose that there is no closed form for a definite integral; for example, :. Compute the surface area for arbitrary endpoint :. Get immediate feedback and guidance with step-by-step solutions for integrals and Wolfram Problem Generator. Restrictions on the domains of the variables and parameters in the integral can be specified using Assumptions.

Wolfram Language Revolutionary knowledge-based programming language.

To use it, load the package, and simply use Int in place of Integrate. Alternatively, you can use Integrate twice:. Use Green's Theorem to find the area of the area enclosed by the following curve:. Region Integrals 11 Integrate a constant over a unit disk:. Line Integrals 6 Compute the line integral of over the origin-centered ellipse with semi-major axes and :. Compare with the answer returned by Area :. Apply the change of variables to a definite integral:. Integrals of Piecewise and Generalized Functions 12 Compute the indefinite integral of a Piecewise function:. Hypergeometric functions such as Hypergeometric2F1 :. The following vector-field has a divergence equal :. RegionMeasure for a region is given by the integral :. Compare with HankelTransform :.