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$\int_{0}^{\frac{1}{90}}-25\sin\left(\frac{7}{2}\pi \cdot 50x- \frac{3}{5}\pi \right)dx$
Learn how to solve definite integrals problems step by step online. \int_0^{\frac{1}{90}}\left(-25\cdot \sin \left(3.5\cdot \pi \cdot \left(50\right)x-0.6\cdot \pi \right)\right)dx. Math interpretation of the question. Simplifying. The integral of a constant times a function is equal to the constant multiplied by the integral of the function. We can solve the integral \int_{0}^{\frac{1}{90}}\sin\left(549.778714x-\frac{3\pi}{5}\right)dx by applying integration by substitution method (also called U-Substitution). First, we must identify a section within the integral with a new variable (let's call it u), which when substituted makes the integral easier. We see that 549.778714x-\frac{3\pi}{5} it's a good candidate for substitution. Let's define a variable u and assign it to the choosen part.