# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\int_{1}^{3}\cos\left(x\right)^2dx$

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

$\int_{1}^{3}\frac{1+\cos\left(2x\right)}{2}dx$

Learn how to solve definite integrals problems step by step online. Integrate cos(x)^2 from 1 to 3. Apply the trigonometric identity: \cos\left(x\right)^2=\frac{1+\cos\left(2x\right)}{2}. Take the constant \frac{1}{2} out of the integral. Divide 1 by 2. Simplifying.

$\frac{149}{212}$$\,\,\left(\approx 0.702822\right)$
$\int_{1}^{3}\cos\left(x\right)^2dx$