Final answer to the problem
$2147483647+\frac{-1\cdot {\left(-121\right)}^{8}}{8}$
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Step-by-step Solution
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1
Calculate the power $2^2$
$\int_{-121}^{4} t\left(t^3+2\right)^2dt$
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$\int_{-121}^{4} t\left(t^3+2\right)^2dt$
Learn how to solve definite integrals problems step by step online. Integrate the function t(t^3+2)^2 from -121 to 2^2. Calculate the power 2^2. Rewrite the integrand t\left(t^3+2\right)^2 in expanded form. Expand the integral \int_{-121}^{4}\left(t^{7}+4t^{4}+4t\right)dt into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-121}^{4} t^{7}dt results in: 8192+\frac{-1\cdot {\left(-121\right)}^{8}}{8}.
Final answer to the problem
$2147483647+\frac{-1\cdot {\left(-121\right)}^{8}}{8}$