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For f(x)=x2(8+x3)10f(x)=x^{2}\left(8+x^{3}\right)^{10} , Find a Function F(x)F(x) Such That F′(x)=f(x)F^{\prime}(x)=f(x) And F(0)=0F(0)=0
A) 133((8+x3)11)\frac{1}{33}\left(\left(8+x^{3}\right)^{11}\right)

Question 62

Multiple Choice

For f(x) =x2(8+x3) 10f(x) =x^{2}\left(8+x^{3}\right) ^{10} , find a function F(x) F(x) such that F′(x) =f(x) F^{\prime}(x) =f(x) and F(0) =0F(0) =0 .


A) 133((8+x3) 11) \frac{1}{33}\left(\left(8+x^{3}\right) ^{11}\right)
B) 133((8+x3) 11−811) \frac{1}{33}\left(\left(8+x^{3}\right) ^{11}-8^{11}\right)
C) 199((8+x3) 11−811) \frac{1}{99}\left(\left(8+x^{3}\right) ^{11}-8^{11}\right)
D) x99(8+x3) 11\frac{x}{99}\left(8+x^{3}\right) ^{11}

Correct Answer:

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