Hello everyone this is Tom from EveryStepCalculus.com, EveryStepPhysics.com. Programs that show you step by step how to do these problems.
A student submitted this to Yahoo and it was– you can see the problem, regarding the trapezoidal rule. And, let’s do it. Index8() to get to my menu. I’m going to scroll up to get right to the bottom of the menu.
Cause the trapezoidal rule, T, is closer to the W’s than the A’s. So I did it that way. There’s the trapezoidal rule there on the menu. And it’s really a trapezoidal rule calculator that’s really what would it involves, pretty neat, too.
We add our function. You have to press alpha before you enter anything into these entry lines here in your calculator. Alpha X squared plus 4 times X. I always show you what you’ve entered, you can change it if you want. I say it’s okay, enter the range. The range is alpha 0 and alpha 4. Looks pretty good.
Remember, that’s a definite integral, you can go to my definite integral program (click) and do the calculation exactly. It’ll give you the same answer as what we’re gonna get here. This is a roundabout way of doing something that’s nonsense in both areas. So I say that’s okay. We’re gonna enter the intervals, which is alpha 4.
And here’s the formula, change of X divided by 2, and then f(a), 2 of F of x1, 2 of F of x2, etcetera, etcetera. Down to f(b). This is the actual formula, no matter how many intervals. Change of x is B-minus a divided by n, so that’s 4 minus 0 divided by 4, turns out to be 1, and we compute the intervals. x0, x1, x3, x4, here’s the answers: 1 and 2 and 3 and 4. and we replace them in the function. F(a) is 0, so we have 0 placed in the function, we’re substituting 0 for every X in the function. And the answer is this right here, 0.
Do the same thing for f(x1) and f(x2). F(1) is placed into the function to equal 5, 12. F(x3) and f(b), so 21 and 32 answer. You’d put parenthesis around these quotation marks, the calculator makes me use quotation marks, but you’re gonna put parenthesis around these, okay, so you look good on your paper. So when we do the definite integral here you’re gonna do the trapezoidal rule approximation. There’s the approximation, and we substitute for these values here.
Put this on your paper and just look like a genius. Do the calculations, comes up to this right here, that turns out to be 54 square units. Pretty neat, huh? EveryStepCalculus.com, go to my site, buy my programs if you wanna pass calculus easy, and subscribe to me if you wanna see more videos and know how my programs work so great. Have a good one.