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Learn how to solve definite integrals problems step by step online.
$\int_{\frac{\pi}{2}}^{\frac{5\pi}{2}} x\sin\left(x\right)^2dx$
Learn how to solve definite integrals problems step by step online. Integrate the function xsin(x)^2 from pi/2 to (5*pi)/2. Simplifying. Apply the trigonometric identity: \sin\left(\theta \right)^2=\frac{1-\cos\left(2\theta \right)}{2}. We can solve the integral \int x\frac{1-\cos\left(2x\right)}{2}dx by applying integration by parts method to calculate the integral of the product of two functions, using the following formula. First, identify u and calculate du.