Final Answer
$\frac{40}{3}$
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Step-by-step Solution
Specify the solving method
1
Rewrite the integrand $x\left(2x+4\right)$ in expanded form
$\int_{0}^{2}\left(2x^2+4x\right)dx$
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$\int_{0}^{2}\left(2x^2+4x\right)dx$
Learn how to solve definite integrals problems step by step online. Integrate the function x(2x+4) from 0 to 2. Rewrite the integrand x\left(2x+4\right) in expanded form. Expand the integral \int_{0}^{2}\left(2x^2+4x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{2}2x^2dx results in: \frac{16}{3}. The integral \int_{0}^{2}4xdx results in: 8.
Final Answer
$\frac{40}{3}$
Exact Numeric Answer
$13.3333$