Evaluate the summation below. 2sum_(t=0)^(3)(4t+t^(2)) Answer:

Write Summation Formula: Write down the summation formula that needs to be evaluated. We need to evaluate the summation 2∑(from t=0 to 3) of (4t + t^2).Expand Summation: Expand the summation by plugging in the values of t from 0 to 3. 2∑(from t=0 to 3) of (4t + t^2) = 2[(4*0 + 0^2) + (4*1 + 1^2) + (4*2 + 2^2) + (4*3 + 3^2)]Calculate Terms: Calculate the terms inside the brackets. 2[(4*0 + 0^2) + (4*1 + 1^2) + (4*2 + 2^2) + (4*3 + 3^2)] = 2[(0 + 0) + (4 + 1) + (8 + 4) + (12 + 9)]Simplify Terms: Simplify the terms inside the brackets. 2[(0 + 0) + (4 + 1) + (8 + 4) + (12 + 9)] = 2[0 + 5 + 12 + 21]Add Numbers: Add the numbers inside the brackets. 2[0 + 5 + 12 + 21] = 2[38]Multiply Sum: Multiply the sum by 2. 2[38] = 76

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Evaluate the summation below.

2sum_(t=0)^(3)(4t+t^(2))
Answer:

Evaluate the summation below. $\newline$ $2 \sum_{t=0}^{3}\left(4 t+t^{2}\right)$ $\newline$ Answer:

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Calculus

Evaluate definite integrals using the chain rule

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Q. Evaluate the summation below.

\newline

2 \sum_{t=0}^{3}\left(4 t+t^{2}\right)

\newline

Answer:

Write Summation Formula: Write down the summation formula that needs to be evaluated. $\newline$ We need to evaluate the summation $2\sum_{t=0}^{3} (4t + t^2)$ .
Expand Summation: Expand the summation by plugging in the values of $t$ from $0$ to $3$ . $2\sum_{t=0}^{3} (4t + t^2) = 2[(4\cdot0 + 0^2) + (4\cdot1 + 1^2) + (4\cdot2 + 2^2) + (4\cdot3 + 3^2)]$
Calculate Terms: Calculate the terms inside the brackets. $\newline$ $2[(4\times0 + 0^2) + (4\times1 + 1^2) + (4\times2 + 2^2) + (4\times3 + 3^2)] = 2[(0 + 0) + (4 + 1) + (8 + 4) + (12 + 9)]$
Simplify Terms: Simplify the terms inside the brackets. $\newline$ $2[(0 + 0) + (4 + 1) + (8 + 4) + (12 + 9)] = 2[0 + 5 + 12 + 21]$
Add Numbers: Add the numbers inside the brackets. $\newline$ $2[0 + 5 + 12 + 21] = 2[38]$
Multiply Sum: Multiply the sum by $2$ . $\newline$ $2[38] = 76$