Integrate. int_(10)^(13)2xdx

Identify Integral: Identify the integral to be solved. We need to evaluate the integral of the function 2x from the lower limit of 10 to the upper limit of 13.Set Up: Set up the integral. The integral we need to solve is ∫(from 10 to 13) 2x dx.Use Power Rule: Use the power rule for integration. The power rule states that the integral of x^n with respect to x is (x^(n+1))/(n+1) + C, where C is the constant of integration. In our case, n=1, so the integral of 2x dx is 2 * (x^(1+1))/(1+1) + C, which simplifies to x^2 + C.Calculate Indefinite Integral: Calculate the indefinite integral. The indefinite integral of 2x dx is x^2 + C.Evaluate Definite Integral: Evaluate the definite integral from 10 to 13. We substitute the upper limit and the lower limit into the indefinite integral and subtract the two results. So, we have (13^2) - (10^2) = 169 - 100 = 69.Write Final Answer: Write the final answer. The value of the integral from 10 to 13 of 2x dx is 69.

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Integrate. $\newline$ $\int_{10}^{13} 2 x d x$

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Calculus

Evaluate definite integrals using the chain rule

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Q. Integrate.

\newline

\int_{10}^{13} 2 x d x

Identify Integral: Identify the integral to be solved. $\newline$ We need to evaluate the integral of the function $2x$ from the lower limit of $10$ to the upper limit of $13$ .
Set Up: Set up the integral. $\newline$ The integral we need to solve is $\int_{10}^{13} 2x \, dx$ .
Use Power Rule: Use the power rule for integration. $\newline$ The power rule states that the integral of $x^n$ with respect to $x$ is $(x^{(n+1)})/(n+1) + C$ , where $C$ is the constant of integration. In our case, $n=1$ , so the integral of $2x \, dx$ is $2 \times (x^{(1+1)})/(1+1) + C$ , which simplifies to $x^2 + C$ .
Calculate Indefinite Integral: Calculate the indefinite integral. $\newline$ The indefinite integral of $2x \, dx$ is $x^2 + C$ .
Evaluate Definite Integral: Evaluate the definite integral from $10$ to $13$ . We substitute the upper limit and the lower limit into the indefinite integral and subtract the two results. So, we have $(13^2) - (10^2) = 169 - 100 = 69$ .
Write Final Answer: Write the final answer. $\newline$ The value of the integral from $10$ to $13$ of $2x \, dx$ is $69$ .