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integration by substitution integration by substitution today we will study integration using u-substitutions so guys as we all know that integration is an important part of mathematics it is one of the key methods by which we can find the area of any region bounded integration includes a function an interval and a real variable this is sometimes also known as definite integrals its general form is f here f is the function x is the real variable and the lower and the upper limit is p and q respectively this general equation basically tells about the area of the graph formed by the function `f on the xy plane and the `x axis with the value of `x lies between p and q which are the given intervals the above written equation can be re written as fxdx fq fp fxdx know more about unbalanced force math.tutorvista.com page no 1/4

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where p and q are the lower limit and upper limit respectively this was the basic part of integration and we get back to the main topic that is integration by u substitution i will give you some basic idea of integration using u-substitution suppose we need to find out the definite integral then first we need to find out the antiderivative of the function which is equal to the actual function f f provided that there should not be any point where no object is defined antiderivative is a process of finding opposite of a derivative which is useful for evaluating a function now in integration using u-substitution the general equation is fxdx fwt w tdt in the first equation the upper limit and the lower limit is wq and wp respectively in the second part of the equation we have substituted x by w and dx/dt by w t which is required for substitution this why the name is given as substitution method now we have to prove that both the sides of the equation are same as to verify the validity of the substitution method so fx dx fwt w t dt we will take the right side of the equation that is fwt w t dt which can also be written as a composite function of the `f an `w and can be represented as fow learn more coefficient of kinetic friction math.tutorvista.com page no 2/4

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now fwt w tdt where upper limit and lower limit are q and p respectively can be written as fow q fow p fwq fxdx fwp with lower limit and upper limit as wp and wq which is the rule of substitution now we will take some examples question 1 answer 1 suppose we have 3x 6 x^2 5x 7dx we need to apply substitution w x^2 5x dw 3x 6dx now we will substitute all the values of x 3x 6 x^2 5x 7dx w^7 this is the required answer of the question above x^2 5x 73x 6dx dw w^8 8 c x^2 5x 8/8 c math.tutorvista.com page no 4/4

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thank you for watching presentation

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