Evaluating a Line Integral In Exercises 19-22, evaluate the line integral along the given path. ∫ C ( x 2 + y 2 + z 2 ) d s C : r ( t ) = sin t i + cos t j + 2 k 0 ≤ t ≤ π 2
Evaluating a Line Integral In Exercises 19-22, evaluate the line integral along the given path. ∫ C ( x 2 + y 2 + z 2 ) d s C : r ( t ) = sin t i + cos t j + 2 k 0 ≤ t ≤ π 2
Solution Summary: The author explains how to calculate the line integral of displaystyle
Evaluating a Line Integral In Exercises 19-22, evaluate the line integral along the given path.
∫
C
(
x
2
+
y
2
+
z
2
)
d
s
C
:
r
(
t
)
=
sin
t
i
+
cos
t
j
+
2
k
0
≤
t
≤
π
2
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY