10 0.8 0.6 0.4 0.2 -1.5 -1.0 -0.5 0.5 1.0 15 where the picture on the left is a graph of e-a² and on the right is e-(*²+v°). If you view the second figure as a solid, the cross-sections are in fact...

Extracted text: 10 0.8 0.6 0.4 0.2 -1.5 -1.0 -0.5 0.5 1.0 15 where the picture on the left is a graph of e-a² and on the right is e-(*²+v°). If you view the second figure as a solid, the cross-sections are in fact circles, and you can treat it as a solid of revolution! (4) In other words, rotate the area under e-a around the y-axis, and show that the volume of the solid of revolution is T. Use this to conclude the value of I.


Extracted text: In this problem we will cover some basic probability theory as an application of integration. We will consider a random variable X, for example the height of a randomly chosen person in our class. Given real numbers a, b, there is a function f called the probability density function such that the probability that X is in the interval (a, b) is equal to P(a < x="">< b)="|" s(12)dæ.="" the="" hydrogen="" atom="" is="" composed="" of="" one="" proton="" in="" the="" nucleus="" and="" one="" electron,="" which="" moves="" about="" the="" nucleus.="" in="" the="" quantum="" theory="" of="" atomic="" structure,="" it="" is="" assumed="" that="" the="" electron="" does="" not="" move="" in="" a="" well-defined="" orbit.="" instead,="" it="" occupies="" a="" state="" known="" as="" an="" orbital,="" which="" may="" be="" thought="" of="" as="" a="" “cloud"="" of="" negative="" charge="" surrounding="" the="" nucleus.="" at="" the="" state="" of="" lowest="" energy,="" called="" the="" ground="" state,="" or="" 1s-orbital,="" the="" shape="" of="" this="" cloud="" is="" assumed="" to="" be="" a="" sphere="" centered="" at="" the="" nucleus.="" this="" sphere="" is="" described="" in="" terms="" of="" the="" probability="" density="" sa?e-2#/a0,="" æ="" 2="" 0="" p(x)="" x=""><0 where="" ao="" is="" the="" bohr="" radius.="" the="" integral="" p(0="">< x="">