![]() And so this is going to be equal to, I think we deserve at leastĪ little mini-drum roll right over here. Alright multiply the numeratorĪnd denominator by four. So this is be four thirds over 12 is 16 over 12. Now let's see the commonĭenominator here would be 12. This is four thirds, four thirds minus oneįourth minus one sixth and then we have plus plus one half. So this is going to be, let's see This is, if we divide, So we're gonna subtract evaluating it at one, it's gonna be one sixth minus one half) And now we just have toĮvaluate these fractions. And when you evaluate it at one, you're gonna have minus And so we get, when you evaluate it at two, you get two to the third, which is eight over six minus one half times one half. Take it, yep negative two and then this one, yep, that looks good. Is that right? Did I do that? Yep, negative one, when you That so minus one half X to the negative one power. And then this is going to be, we're going to increment, this is gonna be X to the negative one. So one half divided by three is one sixth. Let's see it's X to the third and then we divide by three. The anti-derivative of one half X squared that's going to be, what? That's going to be one, ![]() So it's going to be theĭefinite integral of this from X equals one to X equals two D X. ![]() Integral from X equals one to X equals two of this D X. So we're gonna take the definite integral, in this case, from X equals one X equals one to X equals two. If we're gonna take, Let me rewrite this. This is going to be equal to one half, X to the negative two That I could actually recognize, now I couldĭistribute things back. Or I could actually, now that I did all this to put this in a form X to the negative two power times, times X to the fourth plus one. Let me just color code it, this is going to be one half And so that's going to be equal to square root of this is, Times X to the fourth is X to the eighth. And this over here weĬould rewrite this as X to the fourth plus, so we write it this way, this is going to be X to the fourth plus one squared. This is equal to, that same color, one half X to the negative two squared. Because this one, this right over here we could rewrite as one half So plus two X to the fourth, and then this one is So this term right over here, once again, this powering Here, if I factored out a one fourth, it's going to be equal to two X to the fourth. This first term, when you factor this out is going to be X to the eighth power. So this is going to be equal to one fourth X to the negative four times, let's see I factored that out, so if you factor oneįourth X to the negative fourth out of this first term, and I could color-code 'em a little bit. So let's factor out a one fourth X to the negative fourth power. That we could recognize how to factor it a little bit better. Up so that it's a product of perfect squares, because it does look, you know X to fourthĪnd let's see if we can write this in a way One half plus one fourth, plus one fourth X to This is going to beĮqual to X to the fourth over four. One and a minus one half so we can simplify them a little bit. And then this term right over here squared is going to be positive one fourth X to the negative four. ![]() Product of these two and then multiplied that by two, yep, it's just gonna be negative one half. And so it's going to be negative one half. X to the negative two which is going to be one. These times two is going to get us negative, Let's see X squared time Term right here squared is going to be X to the fourth over four. Out what is one plus F prime of X squared? So it's going to be, So one, one plus F prime of X, F prime of X squared is going to be equal to it's gonna be one plus this thing squared. Now, what is F prime of X squared? So it's going to be, Actually let's just write And so that's going toīe negative one half X to the negative two. This is one half X to the negative one is one way to think about it. Over six is going to be X squared over two, and The derivative of that is three X squared. So what is F prime of X going to be? Let's see, X to the third, Need to square it, we need to add one to it, and then we X we just need to figure out what F prime of X is, we Of X we could actually deal in terms of other variables. Lower boundary in X to the upper boundary in X,Īnd this is the arc length, if we're dealing in terms We got arc length, arc length is equal to the integral from the We got a justification for the formula of arc length. The arc length formula correctly, it'll just beĪ bit of power algebra that you'll have to do toĪctually find the arc length. So I encourage you to pause this video and try it out on your own. And so we've already highlighted that in this purple-ish color. Express the value of L in terms of the parameter k. Length along this curve between X equals one and X equals two. You might need: Let L denote the arc length of the graph of the function. And what I want to do in this video is to figure out the arc This right here is the graph of Y is equal to X to the third over six plus one over two X.
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Since he/she is the one going to do the job, their concern should be your topmost priority.Īfter consulting him/her, you then have to do your own research before you choose to buy a particular paint. ![]() There are several types of paint in Ghana and Coral Paint Ghana is undoubtedly one of the best on the market.Īfter reading through this article, you should also ask for your painter’s opinion on the best paint to go for. Kumasi Mall, 1 Lake Road, Asokwa Industrial Area,Īgona, Chapel Square, Opposite TOTAL Filling Station, ![]() We are going to show you some of them and if you want to find out more, you can visit Coral Paint Ghana’s official website for all the places you can buy from.Ĭoral Paint Main Showroom & Head Office, AdabrakaĬommunity 25, Aflao Road, Dawhenya (near Eno spot) You can buy Coral Paint from several places around the country. It comes in 5L which costs GHS 159.80 and the 20L costs GHS 510.60. WALLGUARD: is a suede finish emulsion finish that can be used for exterior walls. WEATHERSHIELD: it is a satin finish emulsion that can be used for exterior walls. The 2.5L costs GHS 52.60 and the 20L costs GHS 401.40. The 2.5L costs GHS 39.00 and the 20L costs GHS 281.20.ĭULUX LUXURIOUS SILK: it is a satin finish emulsion that can be used for interior walls. The 3.6L costs GHS 77.90 and the 18L bucket costs GHS 356.20.ĭULUX ACRYLIC PVA: this is a matt finish emulsion that can be used for interior walls. The price of the paint depends on the size of the container the paint is in.īelow are some of the top paints recommended by Coral Paint Ghana and their prizes.ĬORALATEX: this paint is a matt finish emulsion that can be used for both interior and exterior walls. The average price for paint at Coral Paint Ghana is from GHS 20.00 – GHS 500.00. ![]() As such, we contacted Coral Paint Ghana and they provided us with some of the recommended paints for both interior and exterior paints.Īll other paints are within the same price range. Coral Paint Ghana Exterior PaintsĬoral Paint Ghana has a huge list of paints on their portfolio. Due to a large number of paints that Coral Paint Ghana has in its portfolio, I am just going to show you a few numbers of them. Where Can You Buy Coral Paints in Ghana Coral Paint Ghana Types Of PaintsĬoral Paint Ghana has two (2) types of paints the ones used for interior and the other type is for the exterior. ![]() The cropped video will saved in your Photos library. Click on Crop, scroll your mouse to move the cropping frame, also you can adjust the cropping aspect ratio.Double click the video to open it, hit Edit.Open Photos app on Mac, import the video by drag and drop.How to Crop Video Free on Mac without iMovie? Stick to basic video editing features only.Flip and crop videos with selected aspect ratio.It is a program to showcase photos but with built-in editing tools to perfect photos and videos on Mac. PhotosĪnother native option to crop videos on MacOS but without iMovie is to use Photos app. Once the video playing finishes, click the Recording button to save the cropped video.Ĭrop Video on Mac Free without QuickTime or iMovieĪlso, there are 3 free ways to crop video on Mac without QuickTime or iMovie.Click Start Recording and play the video immediately.In the Options menu, choose the sound output to crop the video with audio kept.Drag the cropping frame to record part of the video.In QuickTime Player app, go to File> New Screen Recording.Open the video you want to crop in QuickTime or other video player, get it ready for playing and pause.How to Crop Video on Mac with QuickTime Player? You have to record the video to crop, the process is time consuming.Though it doesn’t have a crop tool to cut off unwanted parts of your videos, it offers a video cropping solution by using its record feature. QuickTime Player is a stripped-down app for home users to play or record videos in macOS, it has video edit tools like rotate, flip, add clip, remove audio/video, and trim. How to Crop Video on macOS in QuickTime Player Then click Export to save the cropped video on Mac.Then choose a Cropping aspect ratio, 16:9, 4:3, 1:1, 9:16 or use the x:y Settings to crop your video in any dimension/size. 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