For $f(x)=x^{2} e^{10 x}$ , Find a Function $F(x)$ Such That $F^{\prime}(x)=f(x)$ And $F(0)=0$

question 39

Multiple Choice

For $f(x) =x^{2} e^{10 x}$ , find a function $F(x)$ such that $F^{\prime}(x) =f(x)$ and $F(0) =0$ .

• A) \(e^{10 x}\left(\frac{1}{10} x^{2}-\frac{1}{50} x+\frac{1}{500}\right)-\frac{1}{500}\)
• B) \(e^{10 x}\left(\frac{1}{10} x^{2}-\frac{1}{50} x+\frac{1}{500}\right)\)
• C) \(e^{10 x}\left(\frac{1}{10} x^{2}-\frac{1}{50} x\right)\)
• D) \(e^{10 x}\left(\frac{x^{3}}{30}\right)\)