Homework Help is Here – Start Your Trial Now!
Math
Calculus
consider the integral 1² +5) dx 3 x a) Riemann sum using right endpoints and n=4 b) Riemann sum using left endpoints and n=4 11

consider the integral 1² +5) dx 3 x a) Riemann sum using right endpoints and n=4 b) Riemann sum using left endpoints and n=4 11

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 77E
See similar textbooks
icon
Related questions
Question
### Consider the Integral \[ \int_5^9 \left( \frac{3}{x} + 5 \right) dx \] **Tasks:** a) **Riemann Sum using Right Endpoints and \( n = 4 \)** \[ = \] b) **Riemann Sum using Left Endpoints and \( n = 4 \)** \[ = \] ### Explanation: For both tasks, you will need to calculate the Riemann sums for the given integral, which involves approximating the area under the curve using rectangles. 1. **Right Endpoints (n=4):** - Divide the interval \([5, 9]\) into 4 equal subintervals. - Evaluate the function \( \left( \frac{3}{x} + 5 \right) \) at the right endpoint of each subinterval. - Sum up the areas of the rectangles formed by these function values. 2. **Left Endpoints (n=4):** - Divide the interval \([5, 9]\) into 4 equal subintervals. - Evaluate the function \( \left( \frac{3}{x} + 5 \right) \) at the left endpoint of each subinterval. - Sum up the areas of the rectangles formed by these function values. In both cases, ensure to calculate the width of the subintervals and use it in the computation of the area of each rectangle. Then, add these areas to obtain the Riemann sum.
Transcribed Image Text:### Consider the Integral \[ \int_5^9 \left( \frac{3}{x} + 5 \right) dx \] **Tasks:** a) **Riemann Sum using Right Endpoints and \( n = 4 \)** \[ = \] b) **Riemann Sum using Left Endpoints and \( n = 4 \)** \[ = \] ### Explanation: For both tasks, you will need to calculate the Riemann sums for the given integral, which involves approximating the area under the curve using rectangles. 1. **Right Endpoints (n=4):** - Divide the interval \([5, 9]\) into 4 equal subintervals. - Evaluate the function \( \left( \frac{3}{x} + 5 \right) \) at the right endpoint of each subinterval. - Sum up the areas of the rectangles formed by these function values. 2. **Left Endpoints (n=4):** - Divide the interval \([5, 9]\) into 4 equal subintervals. - Evaluate the function \( \left( \frac{3}{x} + 5 \right) \) at the left endpoint of each subinterval. - Sum up the areas of the rectangles formed by these function values. In both cases, ensure to calculate the width of the subintervals and use it in the computation of the area of each rectangle. Then, add these areas to obtain the Riemann sum.
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
SEE MORE TEXTBOOKS