deiru said:Homework Statement
solve the integral ∫[(x^2)/(2^x)]dx evaluating from infinity to 0
Homework Equations
The Attempt at a Solution
using integration by parts I get this: ([(ln(2)x]^2 + 2ln(2)x +2)/(2^x)[ln(2)]^3
and a really big headache
An integral is a mathematical concept that represents the area under a curve on a graph. It is denoted by the symbol ∫ and is used to find the total value of a function over a specific interval.
To solve an integral, you need to use integration techniques such as substitution, integration by parts, or partial fractions. You can also use online tools or software to solve integrals.
The specific integral in this question is ∫ (x^2)/(2^x) dx, which represents the area under the curve of the function (x^2)/(2^x) from a specific lower limit to a specific upper limit.
The limit of integration in this integral is not specified, so it can be solved for any interval. However, common limits of integration are from negative infinity to positive infinity or from 0 to a specific upper limit.
Some common strategies for solving integrals include using integration rules, identifying patterns, and applying trigonometric identities. It is also helpful to simplify the integrand and use techniques such as partial fractions or substitution.