Horton Ayala
11/26/2023 · Primary School
\( \int _ { 1 } ^ { 3 } ( 6 x ^ { 2 } + 4 x ) d x = f ( c ) ( 3 - 1 ) \)
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Step-by-step Solution
Calculate the integral \( \int _ { 1 } ^ { 3 } ( 6 x ^ { 2 } + 4 x ) d x \).
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
\(\int_{1}^{3} 6x^{2}+4x dx\)
- step1: Evaluate the integral:
\(\int 6x^{2}+4x dx\)
- step2: Use properties of integrals:
\(\int 6x^{2} dx+\int 4x dx\)
- step3: Evaluate the integral:
\(2x^{3}+2x^{2}\)
- step4: Return the limits:
\(\left(2x^{3}+2x^{2}\right)\bigg |_{1}^{3}\)
- step5: Calculate the value:
\(68\)
La integral de \( \int _ { 1 } ^ { 3 } ( 6 x ^ { 2 } + 4 x ) d x \) es igual a 68.
Por lo tanto, \( f(c)(3-1) = 68 \), lo que significa que \( f(c) = 34 \).
Quick Answer
La integral es 68, por lo que \( f(c) = 34 \).
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