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I don't understand what the book said. See attached page,

1) The Red underlined section. I don't understand why B will be at it's max negative value at the beginning of the cycle assume it is sine wave start at V=0 at t=0.

2) What is the "subsequent half-cycle? Why is it has to be divided by 2?

3) Notice in the equation, the integration is only for half the cycle from 0 to π/ω? If this is because the result is zero if integrate a full cycle, why is it not having a multiply by 2 in it for the full cycle?

Thanks

1) The Red underlined section. I don't understand why B will be at it's max negative value at the beginning of the cycle assume it is sine wave start at V=0 at t=0.

2) What is the "subsequent half-cycle? Why is it has to be divided by 2?

3) Notice in the equation, the integration is only for half the cycle from 0 to π/ω? If this is because the result is zero if integrate a full cycle, why is it not having a multiply by 2 in it for the full cycle?

Thanks