If the Midpoint Rule is used on the interval \( [-1,17] \) with \( n=3 \) subintervals, at what \( x \)-coordinates is the integrand evaluated? \( \square \) (Simplify your answer. Use a comma to separate answers as needed.)
Solución de inteligencia artificial de Upstudy
Responder
Solución
Respondido por UpStudy AI y revisado por un tutor profesional


The Deep Dive
To apply the Midpoint Rule, we first determine the width of each subinterval. The interval \( [-1, 17] \) has a total length of \( 17 - (-1) = 18 \). Dividing this by \( n = 3 \) gives us a subinterval width \( \Delta x = \frac{18}{3} = 6 \). The subintervals are: 1. From \( -1 \) to \( 5 \) 2. From \( 5 \) to \( 11 \) 3. From \( 11 \) to \( 17 \) The midpoints of these subintervals will be where we evaluate the integrand: 1. The midpoint of the first interval \( [-1, 5] \) is \( \frac{-1 + 5}{2} = 2 \). 2. The midpoint of the second interval \( [5, 11] \) is \( \frac{5 + 11}{2} = 8 \). 3. The midpoint of the third interval \( [11, 17] \) is \( \frac{11 + 17}{2} = 14 \). Hence, the \( x \)-coordinates at which the integrand is evaluated are \( 2, 8, 14 \).
preguntas relacionadas
