Write an Expression for the Function, F(x), With $f^{\prime}(x)=\sin ^{2} x+\sin x$

question 34

Multiple Choice

Write an expression for the function, f(x) , with $f^{\prime}(x) =\sin ^{2} x+\sin x$ and $f(\pi / 3) =8$ .

• A) \(f(x)=8+\int_{0}^{x}\left(\sin ^{2} t+\sin t\right) d t\)
• B) \(f(x)=\int_{\pi / 3}^{x}\left(\sin ^{2} t+\sin t\right) d t-8\)
• C) \(f(x)=8+\int_{\pi / 3}^{x}\left(\sin ^{2} t+\sin t\right) d t\)
• D) \(f(x)=8-\frac{\pi}{3}+\int_{0}^{x}\left(\sin ^{2} t+\sin t\right) d t\)

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