Final Answer
$\frac{11}{30}$
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Step-by-step Solution
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1
Expand the integral $\int_{0}^{1}\left(\frac{4}{5}x^3+2x^2-x\right)dx$ into $3$ integrals using the sum rule for integrals, to then solve each integral separately
$\int_{0}^{1}\frac{4}{5}x^3dx+\int_{0}^{1}2x^2dx+\int_{0}^{1}-xdx$
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$\int_{0}^{1}\frac{4}{5}x^3dx+\int_{0}^{1}2x^2dx+\int_{0}^{1}-xdx$
Learn how to solve problems step by step online. Integrate the function 4/5x^3+2x^2-x from 0 to 1. Expand the integral \int_{0}^{1}\left(\frac{4}{5}x^3+2x^2-x\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{1}\frac{4}{5}x^3dx results in: \frac{1}{5}. The integral \int_{0}^{1}2x^2dx results in: \frac{2}{3}. The integral \int_{0}^{1}-xdx results in: -\frac{1}{2}.
Final Answer
$\frac{11}{30}$
Exact Numeric Answer
$0.3667$