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Rewrite the integrand $x\left(-\frac{1}{36}x^2+\frac{2}{9}x-\frac{7}{36}\right)$ in expanded form
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$\int_{1}^{7}\left(-\frac{1}{36}x^{3}+\frac{2}{9}x^2-\frac{7}{36}x\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function x(-1/36x^2+2/9x+-7/36) from 1 to 7. Rewrite the integrand x\left(-\frac{1}{36}x^2+\frac{2}{9}x-\frac{7}{36}\right) in expanded form. Expand the integral \int_{1}^{7}\left(-\frac{1}{36}x^{3}+\frac{2}{9}x^2-\frac{7}{36}x\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{1}^{7}-\frac{1}{36}x^{3}dx results in: -\frac{50}{3}. The integral \int_{1}^{7}\frac{2}{9}x^2dx results in: \frac{76}{3}.