How to plot Integrals Mathematica -


this integral

http://i.stack.imgur.com/yfcdk.png

is suppose give result of energy. i'm trying graph energy function of time. i'm trying use mathemathica, i'm not getting right graph. graph suppose

http://i.stack.imgur.com/f0uxn.jpg

can me?

the problem showing should not produce graph: 3 integrals added definite integrals , produce number. in other words: t-dependence integrated out, there nothing plot, strictly speaking.

however, can generate plot in following way. clear domain has been cut 3 sections, define piecewise function as integrant:

f[t_] = piecewise[{{50 t, t < 1}, {0, 1 <= t < 3}, {50 t - 200, 3 <= t}}]

next, calculate integral of function starting @ t = 0:

fintegral[t_] = assuming[element[t, reals], integrate[f[t1], {t1, 0, t}]]

note how integral uses dummy integration variable t1 integration 0 t. dummy variable drops out when integral , final result not depend on t1; on t. (btw: assuming necessary tell mathematica t real number , not strange complex number. if don't that, mathematica tries more clever need here).

now can plot integral , plot needed:

plot[{fintegral[t]}, {t, 0, 4}]

-

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