# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_{\frac{\pi }{6}}^{\frac{\pi }{2}} x\cdot\cos\left(x\right)dx$

Learn how to solve definite integrals problems step by step online.

$\displaystyle\int u\cdot dv=u\cdot v-\int v \cdot du$

Learn how to solve definite integrals problems step by step online. Integrate xcos(x) from 0.5235987755982988 to 1.5707963267948966. Use the integration by parts theorem to calculate the integral \int x\cos\left(x\right)dx, using the following formula. First, identify u and calculate du. Now, identify dv and calculate v. Solve the integral.

$\frac{167}{377}$$\,\,\left(\approx 0.4429719389957471\right)$

### Problem Analysis

$\int_{\frac{\pi }{6}}^{\frac{\pi }{2}} x\cdot\cos\left(x\right)dx$

### Main topic:

Definite integrals

~ 0.06 seconds