# how the area is exactly zero?

I was reading this PDF which tries to explain the concept of poles and zeros of Laplace transform.

My question is about FIGURE 32-5(b) on page #591.

I don't understand why the area is said to be zero when, as shown, it should clearly be some negative number. The mentioned PDF does try to give an answer which I don't understand.

Figure (b) shows one of the special cases we have been looking for. When this waveform is multiplied by the impulse response, the resulting integral has a value of zero. This occurs because the area above the x-axis (from the delta function) is exactly equal to the area below (from the rectified sinusoid). The values for σ and ω that produce this type of cancellation are called a zero of the system. As shown in the s-plane diagram of Fig. 32-4, zeros are indicated by small circles.

You can consider it to be a follow-on question to this comment where @AJN tried to explain it further but unfortunately I still couldn't get it. I thought it'd be better to ask it separately. I'd appreciate if you could help me with it?