Using integration find the area of the region bounded by the tangent to the curve 4y=x^2 at the point (2,1) and the lines whose equations are x=2y and x=3y-3
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The equation of the curve is:
y = x² / 4
From point (2,1) and the equations of the two lines, we can get the limits of integration.
We substitute the value of y in each of the two equations to get the limits of integration for the values of x.
x = 2y at y=1 this equals to : x =2 - upper limit
x = 3y - 3 at y =1 this equals to : x=0 lower limit.
Integrating x² / 4 between 0 and 2 we have :
1/4 { x³ /3} from x = 0 to x=2
Substituting in the integral we get :
1/4 × 8/3 = 2/3
Area = 2/3 square units.
y = x² / 4
From point (2,1) and the equations of the two lines, we can get the limits of integration.
We substitute the value of y in each of the two equations to get the limits of integration for the values of x.
x = 2y at y=1 this equals to : x =2 - upper limit
x = 3y - 3 at y =1 this equals to : x=0 lower limit.
Integrating x² / 4 between 0 and 2 we have :
1/4 { x³ /3} from x = 0 to x=2
Substituting in the integral we get :
1/4 × 8/3 = 2/3
Area = 2/3 square units.
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