Final Answer
Step-by-step Solution
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Simplify $\left(x^2\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $2$
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$\int_{0}^{2}\left(pi^4x-x^2\right)^2x^{4}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (pi^4x-x^2)^2x^2^2 from 0 to 2. Simplify \left(x^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2. Rewrite the integrand \left(pi^4x-x^2\right)^2x^{4} in expanded form. Expand the integral \int_{0}^{2}\left(x^{6}pi^{8}-2x^{7}pi^4+x^{8}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{2} x^{6}pi^{8}dx results in: pi^{8}\frac{128}{7}.