Sentence examples for integrating the above from inspiring English sources

Then, integrating the above integral equation from to, noticing that and, we have (2.10).

(51) Integrating the above equation with respect to x once and setting integration constant to zero yield {{phi }_{t}}+int{f ( {{phi }_{x}} ), d{{phi }_{x}}}+{{ bigl( g ( {{phi }_{xx}} ) bigr)}_{x}}=0.

Integrating the above equation with respect to x once and setting integration constant to zero yield {{ ( ln w )}_{xt}}+6delta {{ bigl( {{ ( ln w )}_{xx}} bigr)}^{2}}+delta {{ ( ln w )}_{xxxx}}=0.

Integrating the above two Eqs.

Integrating the above relation, we obtain (3.5).

Integrating the above inequality from 0 to, we have (2.5).

Integrating the above inequality with respect to time yields (2.27).

Integrating the above expression in [ 0, 1 ] yields (3.4).

Integrating the above from to, we get (2.15).

Integrating the above from to, by (2.4) we get (2.21).

By integrating the above inequality on, we get (3.5).