Spencer Ford
04/09/2023 · Senior High School
\( F ( x ) = \int _ { 0 } ^ { x } \frac { t ^ { 2 } } { 9 } d t \)
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Tutor-Verified Answer
Step-by-step Solution
Calculate or simplify the expression \( \int_{0}^{x} \frac{t^{2}}{9} dt \).
Evaluate the integral by following steps:
- step0: Evaluate using formulas and rules:
\(\int_{0}^{x} \frac{t^{2}}{9} dt\)
- step1: Evaluate the integral:
\(\int \frac{t^{2}}{9} dt\)
- step2: Use properties of integrals:
\(\frac{1}{9}\times \int t^{2} dt\)
- step3: Evaluate the integral:
\(\frac{1}{9}\times \frac{1}{3}t^{3}\)
- step4: Calculate:
\(\frac{1}{27}t^{3}\)
- step5: Return the limits:
\(\left(\frac{1}{27}t^{3}\right)\bigg |_{0}^{x}\)
- step6: Calculate the value:
\(\frac{1}{27}x^{3}\)
La integral de \( \frac{t^2}{9} \) desde 0 hasta \( x \) es \( \frac{1}{27}x^3 \).
Quick Answer
La integral es \( \frac{1}{27}x^3 \).
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