Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side. ∫ ( 8 x 3 + 1 2 x 2 ) d x = 2 x 4 − 1 2 x + C
Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side. ∫ ( 8 x 3 + 1 2 x 2 ) d x = 2 x 4 − 1 2 x + C
Solution Summary: The author explains the formula used to prove the statement 'displaystyle int' — the derivative of a function is given as nxn-1.
Integration and Differentiation In Exercises 5 and 6, verify the statement by showing that the derivative of the right side equals the integrand on the left side.
∫
(
8
x
3
+
1
2
x
2
)
d
x
=
2
x
4
−
1
2
x
+
C
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
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.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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