Answer:
Step-by-step explanation:
To find (fg)(x), we have to look at f(x) and g(x) and multiply the two quantities together. We are already given the two quantities individually so all that is left is the multiplication:
If we reorder the terms to go from highest degree to lowest, we get our final answer to be the following:
The area of the triangle with the vertices (0, 5), (2, -2), and (5, 1) by using the calculus is 21 square unit.
We need to find the equation among all possible pairs and then integrate the equations from one co-ordinate to another co-ordinate
Equation of line passing through (0,5) and (2,-2) is
y-5 = [(-2-5)/(2-0)](x-0)
=>y-5 = (-7) /2x
=>y= (-7/2x)+5 -------(eq1)
Equation of line passing through (0,5) and (5,1) is
y-5 = [(1-5) / (5-0)](x-0)
=>y-5 = (-4/5)x
=>y = (-4/5)x+5-------(eq2)
Equation of line passing from (2,-2) and (5,1) is
y-(-2) = [[1 - (-2)] / (5-2)] / (x-2)
=>y+2=(3/3)(x-2)
=>y=x-4--------(eq3)
Now, we use definite integration to find the area between the different equation of line.
So, area enclosed between the equations is given by the
area =[(-4/5)x+5 - (-7/2)x + 5)dx +
[(-4/5)x+5 -(x-4)]dx
=>area=(7/2-4/5)x dx +
((-9/5)x+9)dx
Using properties of integration,
=>area=(27/10)x dx +
(-9/5)x+9)dx
=>area=([27/10)×[5² - 2²])/2 + [ (-9/5)×(5²-1²) ]/2 +9×(5-1)
=>area=(27/20)×(25-4) + (-9/5)×24+9×4
=>area = (27×21)/20 + (-216)/5+ 36
=>area=(567/20) - (216/5) + 36
=>area= [(567-261×4)+(36×20)]/20
=>area=[(567-864)+720]/20
=>area=423/20
=>area=21 square unit.
Hence, area of triangle is 21 square unit.
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