So this is just going to be the integral from zero to six of the absolute value of v of t dt, and then we can type this, actually let me just write it out since you would wanna do this if you're actually taking the test. So it's the integral from zero to six of the absolute value of two sine of e to the t over four plus one, close the absolute value, dt, which is going to be approximately equal to, so once again, we hit math, definite integral. We're going from zero to six of, now we'll hit math again, and then we'll go to number. We see absolute value. The absolute value of two sine of e to the, I'll use x again just because it's easier to use on the calculator, and then I'll close the parentheses on, whoops, let me make sure I do this right. So let me close the parentheses on the sine, and then I have plus one, and then there you go, and then I'm integrating with respect to x approximately 12.573. Now let's do part d. I'll do it right over here, part d. For t between zero and six, the particle changes direction exactly once.