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Question Number 207878 by luciferit last updated on 29/May/24

Answered by Berbere last updated on 30/May/24

$$notwelldefind$$$$g\left(x\right)={\int }_0^{x}f\left(t^4\right)+4t^4{f}^{\prime }\left(t\right))dt?$$$$$$

Answered by Berbere last updated on 30/May/24

$$\int f\left(x^4\right)dx+\int 4x^4{f}^{\prime }\left(x^4\right)dx$$$$\int x.4x^3{f}^{\prime }\left(x^4\right)dx=xf\left(x^4\right)-\int f\left(x^4\right)dx$$$$g\left(x\right)=\int f\left(x^4\right)dx+xf\left(x^4\right)-\int f\left(x^4\right)dx=xf\left(x^4\right)+c$$$$g\left(2\right)=2f\left(16\right)+c=4$$$$c=-4$$$$g(-2)=-12$$

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