Answer:

Step-by-step explanation:
For this case we need to find the following integral:

And for this case we can use the substitution
from here we see that
, and if we solve for x we got
, so then we can rewrite the integral like this:

And if we distribute the exponents we have this:

Now we can do the integrals one by one:

And reordering the terms we have"

And rewriting in terms of x we got:

And that would be our final answer.

Divide both sides of the inequality by 4

Move the constant to the right-hand side and change its sign

Calculate the difference

And we are done solving!!~
Answer:
The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis. ⇒ False
The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis. ⇒ False
Step-by-step explanation:
<em>Let us explain the reflection about the axes</em>
- If a graph is reflected about the x-axis, then the y-coordinates of all points on it will opposite in sign
Ex: if a point (2, -3) is on the graph of f(x), and f(x) is reflected about the x-axis, then the point will change to (2, 3)
- That means reflection about the x-axis change the sign of y
- y = f(x) → reflection about x-axis → y = -f(x)
- If a graph is reflected about the y-axis, then the x-coordinates of all points on it will opposite in sign
Ex: if a point (-2, -5) is on the graph of f(x), and f(x) is reflected about the y-axis, then the point will change to (2, -5)
- That means reflection about the y-axis change the sign of x
- y = f(x) → reflection about y-axis → y = f(-x)
<em>Now let us answer our question</em>
The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis.
It is False because reflection about x-axis change sign of y
The graph of y = -f(x) is a reflection of the graph of y = f(x) in the x-axis
The graph of y = -f(x) is a reflection of the graph of y = f(x) in the y-axis.
It is False because reflection about y-axis change sign of x
The graph of y = f(-x) is a reflection of the graph of y = f(x) in the y-axis
You are given two equations, solve for one variable in one of the equations. Say you solved for x in the second equation. Then, plug in that value of x in the x of the first equation. Solve this (first) equation for y (as it should become apparent) and you'll get a number value. Plug in this numerical value of y into the y of the second equation. Solve for x in the second equation. And there you have it: (x, y)