Questions: ∫₁⁶(5x+1) · dx

∫₁⁶(5x+1) · dx
Transcript text: \(\int_{1}^{6}(5 x+1) \cdot d x\)
failed

Solution

failed
failed
Paso 1: Encontrar la antiderivada

Calculamos la antiderivada de la función \( 5x + 1 \). La antiderivada es: \[ \int (5x + 1) \, dx = \frac{5}{2}x^2 + x + C \]

Paso 2: Evaluar en los límites de integración

Evaluamos la antiderivada en los límites de integración \( x = 6 \) y \( x = 1 \): \[ F(6) = \frac{5}{2}(6)^2 + (6) = \frac{5}{2} \cdot 36 + 6 = 90 + 6 = 96 \] \[ F(1) = \frac{5}{2}(1)^2 + (1) = \frac{5}{2} \cdot 1 + 1 = \frac{5}{2} + 1 = \frac{5}{2} + \frac{2}{2} = \frac{7}{2} \]

Paso 3: Restar los resultados

Restamos los valores obtenidos en los límites de integración: \[ \int_{1}^{6} (5x + 1) \, dx = F(6) - F(1) = 96 - \frac{7}{2} \] Para realizar la resta, convertimos \( 96 \) a fracción: \[ 96 = \frac{192}{2} \] Entonces: \[ \int_{1}^{6} (5x + 1) \, dx = \frac{192}{2} - \frac{7}{2} = \frac{192 - 7}{2} = \frac{185}{2} \]

Respuesta Final

\(\boxed{\frac{185}{2}}\)

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
What is the shape of the relationship between mean attendance and player value?
failedAnswered
A reaction below produced nickel tetracarbonyl, Ni(CO)4 in a 88% yield. Assuming sufficient nickel metal was used, what mass of carbon monoxide, CO, was added to the reaction if the actual yield of product, Ni(CO)4, was 185 g? Hint: Calculate the theoretical yield of nickel tetracarbonyl from the percent yield and work backwards from there. 4 CO(g)+Ni(s) -> Ni(CO)4(l) - For CO, 28.0 g / mol - For Ni(CO)4, 170.7 g / mol
failedAnswered
"We really should try that recipe. Someone told me that it was good." Is this an ethos?
failedAnswered
What tRNA anti-codon would match the mRNA codon -U-A-C-? -A-U-G- -U-T-C- -T-A-C- -U-A-C-
failedAnswered
A university conducted a survey of 373 undergraduate students regarding satisfaction with student government. Results of the survey are shown in the table by class rank. Complete parts (a) through (d) below. (a) If a survey participant is selected at random, what is the probability that he or she is satisfied with student government? P( satisfied )= (Round to three decimal places as needed.) (b) If a survey participant is selected at random, what is the probability that he or she is a junior? P (junior) = (Round to three decimal places as needed.) (c) If a survey participant is selected at random, what is the probability that he or she is satisfied and a junior? P( satisfied and junior )= (Round to three decimal places as needed.) (d) If a survey participant is selected at random, what is the probability that he or she is satisfied or a junior? P( satisfied or junior )= (Round to three decimal places as needed.)