Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Discover a wealth of knowledge from experts across different disciplines on our comprehensive Q&A platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
Answer:
Step-by-step explanation:
∫41 xh''(x)dx=41[x∫h''(x)dx-∫{1∫h''(x)dx}dx]+c
The value of [tex]\int\limits^{4}_{1} {x\cdot h''(x)} \, dx[/tex] is 8.5. The choice that represent the best approximation is A.
How to determine the result of a definite integral based on a formula and a table
This integral can be approximated by the following Riemann sum:
[tex]A = \Sigma\limits_{i=0}^{2} \left\{(x_{i+1}-x_{i})\cdot x_{i}\cdot h''(x_{i})+\frac{1}{2}\cdot (x_{i+1}-x_{i})\cdot [x_{i+1}\cdot h''(x_{i+1})-x_{i}\cdot h''(x_{i})] \right\}[/tex]
[tex]A = \frac{1}{2} \cdot \Sigma\limits_{i=0}^{2} \left\{(x_{i+1}-x_{i})\cdot [x_{i+1}\cdot h''(x_{i+1})+x_{i}\cdot h''(x_{i})] \right\}[/tex]
Then, the approximate value of the integral is:
[tex]A = \frac{1}{2}\cdot \{(2-1)\cdot [(2)\cdot 2+(1)\cdot (-5)]+(3-2)\cdot [(3)\cdot 1+(2)\cdot 2]+(4-1)\cdot [(4)\cdot 2+(3)\cdot 1]\}[/tex]
[tex]A = 8.5[/tex]
The value of [tex]\int\limits^{4}_{1} {x\cdot h''(x)} \, dx[/tex] is 8.5. The choice that represent the best approximation is A. [tex]\blacksquare[/tex]
Remark
The statement is incomplete and poorly formatted and table is missing. Complete statement is:
Selected values of the twice-differentiable function and its first and second derivatives are:
Function
[tex]h(1) = 3[/tex], [tex]h(2) = 6[/tex], [tex]h(3) = 2[/tex], [tex]h(4) = 10[/tex]
First derivative
[tex]h'(1) = 4[/tex], [tex]h'(2) = -4[/tex], [tex]h'(3) = 3[/tex], [tex]h'(4) = 5[/tex]
Second derivative
[tex]h''(1) = -5[/tex], [tex]h''(2) = 2[/tex], [tex]h''(3) = 1[/tex], [tex]h''(4) = 2[/tex]
Selected values of the twice-differentiable function [tex]h[/tex] and its first and second derivatives are given in the table above. What is the value of [tex]\int\limits^{4}_{1} {x\cdot h''(x)} \, dx[/tex]?
A. 9, B. 13, C. 23, D. 38
To learn more on Riemann sums, we kindly invite to check this verified question: https://brainly.com/question/21847158
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.
