Sentence examples for a change of integration from inspiring English sources

We used a change of integration order in an integral, which does not follow from the classic Fubini theorem.

Performing the average in the above equation and performing a change of integration variables, we can write.

Using the transformation result (7) in Appendix A and a change of integration variable, we can write where p0 denotes the 012 allele coding system.

According to the transformation result (8) in Appendix A and a change of integration variable, the conditional expectation of the general mean is (2) where p0 denotes density for the 012 allele coding, and is the conditional expectation of the general mean when using the 012 allele coding.

The second equality uses a change of variables (integration by substitution),.

(3.4) Multiplying both sides of (3.4) by (e^{frac{-x^{2}}{ 4gamma}}), we integrate the results with respect to x from 0 to ∞, and make a change of order of integration in the repeated integral.

For the lower bound (L_{b}), a change of order of integration gives frac{L_{b}}{M-m}=int limits _{b-ell }^{b}left( int limits _{x}^{b}wleft( uright) mathrm{d}_{alpha }uright) mathrm{d}_{alpha }x=Q_{alpha }left( ell,bright) -left( b-ell right) ^{alpha }P_{alpha }left( ell,bright), (3.14 where (P_{alpha }left( ell,bright)) and (Q_{alpha }left( ell,bright)) are described in Definition 3.2.

which after a change of the order of integration can be transformed into (58).

Applying two times the change of integration for triple integrals we have ∫ T ∞ a t ∫ t ∞ b s ∫ s ∞ c τ Δ τ Δ s Δ t = ∫ T ∞ c t ∫ T σ t b s ∫ T σ s a τ Δ τ Δ s Δ t.

The following result is the nabla version of the result obtained in [20]: (change of integration order) Let (fin C_{ld}(mathbb {T}^{2})), then int_{s}^{t}int_{s}^{eta}f eta, zeta)nablazetanablaeta=int_{s}^{t} int_{rho zeta)}^{t} f eta, zeta)nablaetanablazeta quadmbox{for } s,tin mathbb {T}.

The effect of treatment was expressed as a fold change of trophoblast integration area relative to untreated co-culture controls from the same experiment.