 In this video, we provide the solution to question number three for practice exam number two for math 1220, in which case we're given a function in the form of a table here, here's f of x, and some of the entries for x are provided here with their corresponding y coordinates. And then we're supposed to use this table of values for the function f and use it to approximate the integral from 10 to 30, which you'll notice is the first and last entries of this table here. So we want to approximate the integral from 10 to 30 of f of x dx using the trapezoidal rule t sub five here. So let's first calculate what would our delta x look like in that situation delta x would equal 30 minus 10 over five. So we end up with 20 over five delta x is for notice that the tables already set up this way. Now, for all tests, it might not be so simple, but this one does increment by four like so. And so using the trapezoid rule t five, we're going to end up with delta x divided by two times the first entry, which is negative two, plus two times the next negative six, plus two times the next negative two, plus two times. The next which is one plus two times three, plus the last one no two on that one. So we just seek to try to simplify this thing of course delta x like we saw a moment ago was four so we get four over two. Negative 12 plus eight, of course, is going to give us a negative four in that situation. As all of these numbers are divisible by two, I'm going to factor out the two for a moment, and then add these together negative six minus two is a negative eight plus one is a negative seven plus three is a negative four. So we get something like that for divided by two is the same thing as two. Here, we get negative four, so we're going to get two times negative four, which is a negative eight. So we had two times negative 12. And then lastly, our calculation turns out to be negative 24. And so we see that the correct answer would then be choice E.