a. Parameterize 
by
with 
.
b/c. The line integral of 
over is
d. Notice that we can write the line integral as
By Green's theorem, the line integral is equivalent to
where 
is the triangle bounded by , and this integral is simply twice the area of . is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.
Although x ² and x both have the variable x, you can’t add them together. So x + x + x + x is 4x and we just leave x ² the same. So the simplified expression is x ² + 4x. I hope this helped!!
In order to utilize the graph, first you have to distinguish which graph accurately pertains to the two functions.
This can be done by rewriting the equations in the form y = mx + b which can be graphed with ease; where m is the slope and b is the y intercept.
-x^2 + y = 1
y = x^2 + 1
So this will be a basic y = x^2 parabola where the center intercepts on the y axis at (0, 1)
-x + y = 2
y = x +2
So this will be a basic y = x linear where the y intercept is on the y axis at (0, 2)
The choice which depicts these two graphs correctly is the first choice. The method to find the solutions to the system of equations by using the graph is by determining the x coordinate of the points where the two graphed equations intersect.
You would do parentheses first and that answer you will x 7
70 + 1 = 71
Hope I Helped!
