Mathematics, 11.07.2019 23:00 Kurlyash
Calculus: asap evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 4 times x to the 6th power plus 2 times x and 12 times x to the 5th power plus 1, dx. your work must include the use of substitution and the antiderivative.
Answers: 1
![\bf \textit{now, we'll change the bounds, using u(x)} \\\\\\ u(-1)=4(-1)^6+2(-1)\implies u(-1)=2 \\\\\\ u(0)=4(0)^6+2()\implies u(0)=0\\\\ -------------------------------\\\\ \displaystyle \cfrac{1}{2}\int\limits_{2}^{0}~u^3\cdot du\implies \left. \cfrac{1}{2}\cdot \cfrac{u^4}{4} \right]_{2}^{0}\implies \left. \cfrac{u^4}{8} \right]_{2}^{0}\implies [0]-[2]\implies -2](/tpl/images/0078/7557/7285b.png)
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