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ilate
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There are 5 letters in ILATE ( A1E1I1L1T1 )
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Ilate might refer to |
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In calculus, and more generally in mathematical analysis, Integration by parts or partial integration is a process that finds the integral of a product of functions in terms of the integral of their derivative and antiderivative. It is frequently used to transform the antiderivative of a product of functions into an antiderivative for which a solution can be more easily found. The rule can be derived in one line simply by integrating the product rule of differentiation. * If u = u(x) and du = u′(x) dx, while v = v(x) and dv = v′(x) dx, then integration by parts states that:* * * * * * * * * ∫ * * a * * * b * * * u * ( * x * ) * * v * ′ * * ( * x * ) * * d * x * * * * = * [ * u * ( * x * ) * v * ( * x * ) * * ] * * a * * * b * * * − * * ∫ * * a * * * b * * * * u * ′ * * ( * x * ) * v * ( * x * ) * d * x * * * * * * * = * u * ( * b * ) * v * ( * b * ) * − * u * ( * a * ) * v * ( * a * ) * − * * ∫ * * a * * * b * * * * u * ′ * * ( * x * ) * v * ( * x * ) * * d * x * * * * * * * {\displaystyle {\begin{aligned}\int _{a}^{b}u(x)v'(x)\,dx&=[u(x)v(x)]_{a}^{b}-\int _{a}^{b}u'(x)v(x)dx\\&=u(b)v(b)-u(a)v(a)-\int _{a}^{b}u'(x)v(x)\,... |