The primitive function for
is given by it's indefinite integral.
To calculate it, recall:
![\frac{d}{dx}e^{ax}=ae^{ax}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7De%5E%7Bax%7D%3Dae%5E%7Bax%7D)
![\int c f(x)dx = c\int f(x)dx](https://tex.z-dn.net/?f=%5Cint%20c%20f%28x%29dx%20%3D%20c%5Cint%20f%28x%29dx)
Let's begin
![\int 4e^{2x}+e^{-x}dx \\4\int e^{2x}dx+ \int e^{-x}dx\\4\frac{e^{2x}}{2}+\frac{e^{-x}}{-1} + c\\](https://tex.z-dn.net/?f=%5Cint%204e%5E%7B2x%7D%2Be%5E%7B-x%7Ddx%20%5C%5C4%5Cint%20e%5E%7B2x%7Ddx%2B%20%5Cint%20e%5E%7B-x%7Ddx%5C%5C4%5Cfrac%7Be%5E%7B2x%7D%7D%7B2%7D%2B%5Cfrac%7Be%5E%7B-x%7D%7D%7B-1%7D%20%20%2B%20c%5C%5C)
![F(x) = 2e^{2x}-e^{-x} +c](https://tex.z-dn.net/?f=F%28x%29%20%3D%202e%5E%7B2x%7D-e%5E%7B-x%7D%20%2Bc)
To find the costant, we just need to use the fact that ![F(0)=2](https://tex.z-dn.net/?f=F%280%29%3D2)
![F(0) = 2 \\4e^{0}+e^{0} + c =2\\5+c =2\\c=-3](https://tex.z-dn.net/?f=F%280%29%20%3D%202%20%5C%5C4e%5E%7B0%7D%2Be%5E%7B0%7D%20%2B%20c%20%3D2%5C%5C5%2Bc%20%3D2%5C%5Cc%3D-3)
Therefore,
![\boxed{F(x) = 2e^{2x} - e^{-x} -3 }](https://tex.z-dn.net/?f=%5Cboxed%7BF%28x%29%20%3D%202e%5E%7B2x%7D%20-%20e%5E%7B-x%7D%20-3%20%7D)
Answer:
trapezoid area = ((sum of the bases) ÷ 2) • height
trapezoid area = ((6 + 12) / 2) * height
trapezoid area = 18 / 2 * height
height = 99/9 = 11
Step-by-step explanation:
Slope for (x₁, y₁) and (x₂, y₂): (6, 2) and (7, 4)
Slope: (y₂ -y₁) / (x₂ -x₁)
Slope: ( 4 - 2) / (7 - 6) = 2/1
<span>Slope = 2/1 = 2
Option D</span>
Answer:
450
Step-by-step explanation:
60 x 7.5=450