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geerky42

  • 3 years ago

\[\Large\displaystyle \int t^2 \left( t - \dfrac{2}{t} \right) dt\]

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  1. UnkleRhaukus
    • 3 years ago
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    \[=\int (t^3-2t)\mathrm dt\]\[=\int t^3\mathrm dt-2\int t\mathrm dt\]

  2. geerky42
    • 3 years ago
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    Hmm, I should have done that. Thanks.

  3. some_someone
    • 3 years ago
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    I[t^(2)(t-(2)/(t)),t] Remove all extra parentheses from the expression. I[,,t^(2)(t-(2)/(t)),t] To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is t. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions. I[,,t^(2)(t*(t)/(t)-(2)/(t)),t] Complete the multiplication to produce a denominator of t in each expression. I[,,t^(2)((t^(2))/(t)-(2)/(t)),t] Combine the numerators of all expressions that have common denominators. I[,,t^(2)((t^(2)-2)/(t)),t] Divide each term in the numerator by the denominator. I[,,t^(2)((t^(2))/(t)-(2)/(t)),t] Reduce the expression (t^(2))/(t) by removing a factor of t from the numerator and denominator. I[,,t^(2)(t-(2)/(t)),t] To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is t. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions. I[,,t^(2)(t*(t)/(t)-(2)/(t)),t] Complete the multiplication to produce a denominator of t in each expression. I[,,t^(2)((t^(2))/(t)-(2)/(t)),t] Combine the numerators of all expressions that have common denominators. I[,,t^(2)((t^(2)-2)/(t)),t] Divide each term in the numerator by the denominator. I[,,t^(2)((t^(2))/(t)-(2)/(t)),t] Reduce the expression (t^(2))/(t) by removing a factor of t from the numerator and denominator. I[,,t^(2)(t-(2)/(t)),t] Multiply t^(2) by each term inside the parentheses. I[,,t^(3)-2t,t] To find the integral of t^(3), find the anti-derivative. The formula for the anti-derivative of a basic monomial is I[x^(n)=(x^(n+1))/((n+1)),x]. (t^(4))/(4)+I[,,-2t,t] The indefinite integral also has some unknown constant. This can be proven by completing the opposite operation (derivative) in which C would go to 0. The value of C can be found in cases when an initial condition of the function is given. (t^(4))/(4)+I[,,-2t,t]+C To find the integral of -2t, find the anti-derivative. The formula for the anti-derivative of a basic monomial is I[x^(n)=(x^(n+1))/((n+1)),x]. (t^(4))/(4)-t^(2) The indefinite integral also has some unknown constant. This can be proven by completing the opposite operation (derivative) in which C would go to 0. The value of C can be found in cases when an initial condition of the function is given. (t^(4))/(4)-t^(2)+C

  4. some_someone
    • 3 years ago
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    so, (t^(4))/(4)-t^(2)+C

  5. geerky42
    • 3 years ago
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    It's a little too much, but thank you for your effort.

  6. UnkleRhaukus
    • 3 years ago
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    @some_someone Say what?

  7. some_someone
    • 3 years ago
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    I evaluated the integral, isnt that what you wanted @geerky42

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