To solve the given integral ∫π2πθ, we can integrate the variable θ with respect to itself over the specified interval.Using the power rule of integration, which states that ∫xndx=xn+1n+1, we can integrate θ as follows:∫π2πθdθ=θ22|π2πEvaluating the definite integral at the upper and lower limits, we have:((2π)22)−(π22)Simplifying, we get:4π22−π222π2−π224π22−π223π22Therefore, the value of the integral ∫π2πθ is 3π22.

"∫π2πθ" was answered by our community

Aman Jha

Answered question

2022-09-13

$\int_{π}^{2 π} θ$

Answer & Explanation

star233

Skilled2023-05-29Added 403 answers

To solve the given integral

\int_{π}^{2 π} θ

, we can integrate the variable

θ

with respect to itself over the specified interval.
Using the power rule of integration, which states that

\int x^{n} d x = \frac{x^{n + 1}}{n + 1}

, we can integrate

θ

as follows:

\int_{π}^{2 π} θ d θ = \frac{θ^{2}}{2} |_{π}^{2 π}

Evaluating the definite integral at the upper and lower limits, we have:

(\frac{(2 π)^{2}}{2}) - (\frac{π^{2}}{2})

Simplifying, we get:

\frac{4 π^{2}}{2} - \frac{π^{2}}{2}

2 π^{2} - \frac{π^{2}}{2}

\frac{4 π^{2}}{2} - \frac{π^{2}}{2}

\frac{3 π^{2}}{2}

Therefore, the value of the integral

\int_{π}^{2 π} θ

\frac{3 π^{2}}{2}

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