Answer:
![x -3e^{-x} + C](https://tex.z-dn.net/?f=x%20-3e%5E%7B-x%7D%20%2B%20C)
Step-by-step explanation:
Given the integral
, we are to evaluate it. Note that sum of integral is equal to the integral of its individual sum as shown;
![\int\limits {\dfrac{e^{x}+3}{e^x} } \, dx = \int\limits {\dfrac{e^{x}}{e^x} } \, dx + \int\limits {\dfrac{3}{e^x} } \, dx](https://tex.z-dn.net/?f=%5Cint%5Climits%20%7B%5Cdfrac%7Be%5E%7Bx%7D%2B3%7D%7Be%5Ex%7D%20%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%20%7B%5Cdfrac%7Be%5E%7Bx%7D%7D%7Be%5Ex%7D%20%7D%20%5C%2C%20dx%20%2B%20%5Cint%5Climits%20%7B%5Cdfrac%7B3%7D%7Be%5Ex%7D%20%7D%20%5C%2C%20dx)
![= \int\limits 1\, dx + 3\int\limits {e^{-x} \, dx \\\\](https://tex.z-dn.net/?f=%3D%20%5Cint%5Climits%201%5C%2C%20dx%20%2B%203%5Cint%5Climits%20%7Be%5E%7B-x%7D%20%5C%2C%20dx%20%5C%5C%5C%5C)
![= x + 3(-e^{-x})\\\\= x -3e^{-x} + C](https://tex.z-dn.net/?f=%3D%20x%20%2B%203%28-e%5E%7B-x%7D%29%5C%5C%5C%5C%3D%20x%20-3e%5E%7B-x%7D%20%2B%20C)
<em>Hence the value of the evaluated integral is </em>
<em> where C is the constant of integration.</em>
Answer:
3.1, 4.1, 5.1,6.1, 7.1, 8.1, 9.1
Step-by-step explanation:
the bolded numbers are the answer :)
It is not true for expressions with negative exponents
Answer:
-7
Step-by-step explanation:
4x=-28
We need to divide both sides by 4 to make it even.
=![\frac{28\\}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B28%5C%5C%7D%7B4%7D)
x=7
<u>Answer:</u>
Minimum possible area = 6.75 km^2
Maximum possible area = 13.75 km^2
<u>Step-by-step explanation:</u>
This question relates to significant figures so assuming that each of the given values is rounded off to the nearest kilometer.
So we can find the minimum and maximum possible areas of the rectangle.
Minimum possible area of rectangle = 1.5 × 4.5 = 6.75 square kilometers
Maximum possible area of rectangle = 2.5 × 5.5 = 13.75 square kilometers