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Solving MIT INTEGRATION BEE question.
Solving MIT INTEGRATION BEE question.
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The aim of this video is to prove that a subjective function has some properties. First. What's a subjective function? How can we Define a subjective function? How do we know that a function is search active? In this video? We're going to give a An example Of a subjective function, and we're going to prove that it is subjective. We're going to use many algebraic techniques to prove. The following result, The aim is to prove that f is subjective by using algebra and the definition of the subjectivity of the function. We're going to use algebra to prove that the set of images. That means the order range is covered by. I the set of the domain of definition of this function, So we can prove in this case that for every element in the domain We can find, or we can prove that every element in the range. It's covered by some element in the, To the main of definition. Or we can prove that the image of the domain of definition is the whole range. So in this case, we can see that our function is search ejective. Sometimes it's not easy to prove that a function is subjective. We will use some techniques. And in this video this is one of the techniques that we can use to prove that f is subjective To prove this case. We use the fact that if we can show that the set of the old range is covered by all the element of the domain. Our function is subjective. Okay? So this is a nice example to try to train and work, some ideas using algebra and techniques from calculus one, And some pre-calculus, and maybe some algebra two techniques.


We're gonna solve some integration, big questions. So the integration here in these MIT questions Requires some knowledge of the techniques of integration Like integration by part integration by change of variable and geometric interpretation of the integral. Sometimes it's good to have that in in our hat. So, the problem that we're gonna have here is that we will use the cosine and the sine formula for the sum to make the the, this integrand, very easy to solve And that's how we're going to deal with this because sometimes making it easier without the powers and the square root will make the integral, very simple to evaluate and to have. So this is the key idea that we're going to use to make this m, i t integration question very easy to solve