The Integrator block supports vector signals. So, try this...
1. Add an Integrator block to the model. Set the initial condition of the Integrator block to be a vector of n elements, one for each of the equations you'd like to integrate. The input to the Integrator is df/dt, and the output is f.
2. Calculate df/dt. To do this, you will have to use a Gain block to multiply f by a the V vector. By default, the Gain block will use element-wise multiplication, and so each equation would be multiplied by the correct v parameter.
Hope this helps!
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