Determine the coordinates of the centroid of the shaded...

Transcript

00:01 In this question we need to find out what is the coordinates of the centroid of this cent shaded region okay so let us see first of all we have this line l and this curve as c whose equation is y is equals to kx square okay so i will now write down what is the equation of this line equation of l which passes through the two points so the point having coordinate is b comma 2a and this coordinate you can see it as 0 comma a so it passes through b comma 2a and 0 comma a so equation will be y minus a over x minus 0 is equals to y 2 minus y 1 that is 2a minus a over b minus 0 so we are getting y minus a over x is equals to a over b which implies y is equals to ax over b plus a this is what i get or we can simplify it as ax plus ab over b so this is the equation of line that we are getting then what i can do equation of parabola we already have now what i am going to do so let the coordinate of centroid that we have to find out let it be equals to x bar and y bar so x bar will be nothing but integral of xda over two times of this is not integral over two times of da so here what we are actually going to consider so this is our shaded region that we have been given we will consider one thin string so let's say this is our thin strip and this distance we already know it is given to be 2a and this distance is given to be b so from this what i will get for the thin strip let's call this as equation one what we get da will be equals to dx time ax plus ab over b minus kx square because line is above so this minus this cut this is what we will get the area hence we will now use equation number one put this value of da to calculate the x coordinate so it will be nothing but integral from zero to b x is varying from zero to b x times of da which is nothing but ax plus ab over b minus k times of x square times dx over integral of zero to b and here what we are having bx or we can say kx plus ab over b minus kx square dx that is what we are having now we can easily…

Question

Determine the coordinates of the centroid of the shaded area. y y = kx^2 a a b x

Question

Determine the coordinates of the centroid of the shaded area. y y = kx^2 a a b x

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