Now the integral in the November 11,2013, post — that was difficult.

2013 年 11 月 11 日提问的积分就很难。

So, the integral for side three equals zero.

因此，第三边的积分等于零。

That circle in the integral sign is confusing.

积分符号中的那个圆圈令人困惑。

But the integral part is a Scotch Porter Hair Balm.

但不可或缺的部分是 Scotch Porter Hair Balm。

But the integral part is the Scotch Porter Hair Balm.

但不可或缺的部分是 Scotch Porter Hair Balm。

So, the integrals for sides two and four also equal zero.

因此，第二边和第四边的积分也等于零。

It just means the integral is over a closed  surface.

它只是意味着积分是在一个封闭的曲面上。

But here, the integral will always equal zero for a closed surface.

但在这里，对于闭合曲面，积分始终为零。

So, first, let's find its velocity -- the middle step -- by taking the integral of its acceleration.

所以，首先，让我们看看它的速度… … 中间步骤 通过取加速度积分。

Now we're left with the integral of the magnetic field, B, with respect to the points along the circle.

现在我们剩下磁场 B 相对于沿圆的点的积分。

In these cases, we might know what the SHAPE of the integral should look like on a graph

在这些情况下，我们可能知道采取什么形式 它看起来像图表上的积分。

And the integral of ds is just the length of side one of the Amperian rectangle.

ds 的积分就是安培矩形第一条边的长度。

Take the integral of both sides.

对两边取积分。

Instead, you need to take the integral of the pressure with respect to volume.

W=P delta V，因为压力在变化。但你必须 取压力相对于体积的积分。

In other words: B is constant, so we can move it in front of the integral sign.

B是一个常数，所以我们可以移动 所以在积分符号前面。

In a similar way, the work done by a torque is the integral of that torque over a certain angle.

以类似的方式，之前执行的工作 扭矩是给定角度的扭矩积分。

So we put a C in the integral instead, to represent all those options.

所以我们把 C 放在积分中，来表示 所有这些选项。

Electric flux equals the integral of the dot product of electric field and dA.

电通量等于电场与dA的点积的积分。

So, we can take electric field out from under the integral.

因此，我们可以从积分中去除电场。

Anything times 1 is equal to itself, so we can just knock the cosine of theta term out of the integral.

乘以任何 1 等于它自己，所以我们可以将 theta 范围的余弦乘以积分。