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We utilize the integral when both the pressure and volume of a system are changing. This is because if we have a system with constant pressure and a change in volume, the integral would basically be the area of the rectangle which is P*(delta)V and no need to use calculus. If the pressure in changing and volume is constant, then there is no area under the curve to really calculate, and so it is zero. However, when both change, our graph now has a curve, which would require calculus in order to calculate work, and thus the integral comes in handy.
faithkim1L wrote:Do we need to know the integral and derivative for the midterm?
Im not 100% sure considering we haven't gone over a problem using integrals in class, but I think you should definitely try and study it. If you need help Dr.Lavelle has a page on his website titled "Common Antiderivatives" which shows some applications we might see on the midterm
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