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Expand the integral $\int_{a}^{b}\left(4x^3+\frac{2}{7}x\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int_{a}^{b}4x^3dx+\int_{a}^{b}\frac{2}{7}xdx$
Learn how to solve definite integrals problems step by step online. Integrate the function 4x^3+2/7x from a to b. Expand the integral \int_{a}^{b}\left(4x^3+\frac{2}{7}x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{a}^{b}4x^3dx results in: 4\left(\frac{b^{4}}{4}+\frac{-a^{4}}{4}\right). Multiply the single term \frac{2}{7} by each term of the polynomial \left(\frac{1}{2}b^2-\frac{1}{2}a^2\right). The integral \int_{a}^{b}\frac{2}{7}xdx results in: \frac{1}{7}b^2-\frac{1}{7}a^2.