Estimating a definite integral Use a calculator and midpoint Riemann sums to approximate ∫ 1 25 2 x − 1 d x . Present your calculations in a table showing the approximations for n = 10 , 30. and 60 subintervals, assuming a regular partition. Make a conjecture about the exact value of the integral and verify your conjecture using the Fundamental Theorem of Calculus.
Estimating a definite integral Use a calculator and midpoint Riemann sums to approximate ∫ 1 25 2 x − 1 d x . Present your calculations in a table showing the approximations for n = 10 , 30. and 60 subintervals, assuming a regular partition. Make a conjecture about the exact value of the integral and verify your conjecture using the Fundamental Theorem of Calculus.
Solution Summary: The author explains how to approximate a definite integral by using calculator and midpoint Riemann sum. The exact value of the integral is 114.
Estimating a definite integral Use a calculator and midpoint Riemann sums to approximate
∫
1
25
2
x
−
1
d
x
. Present your calculations in a table showing the approximations for
n
=
10
, 30. and 60 subintervals, assuming a regular partition. Make a conjecture about the exact value of the integral and verify your conjecture using the Fundamental Theorem of Calculus.
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.
Question 2.
i. Suppose that the random variable X takes two possible values 1 and -1, and P(X = 1) =
P(X-1)=1/2. Let Y=-X. Are X and Y the same random variable? Do X and Y
have the same distribution? Explain your answer.
ii. Suppose that the random variable X~N(0, 1), let Y=-X. Are X and Y the same random
variable? Do X and Y have the same distribution? Explain your answer.
Problem 4. Let
f(x, y) =
{
Find P(X <1/2|Y = 1/2).
c(x + y²) 0
Qize
f(x)
x + 2x2 - 2
x² + 4x² - 4
Solve the equation using Newton
Raphson
Chapter 5 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
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