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Solve the product $-\frac{1}{8}\left(16-x^2\right)$
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$\int_{0}^{4}\left(\sqrt{16-x^2}-2+\frac{1}{8}x^2\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (16-x^2)^1/2-1/8(16-x^2) from 0 to 4. Solve the product -\frac{1}{8}\left(16-x^2\right). Expand the integral \int_{0}^{4}\left(\sqrt{16-x^2}-2+\frac{1}{8}x^2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\sqrt{16-x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above.