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{:[F(x)=int_(-2)^(sin(x))3tdt],[F^(')(x)=]:}

F(x)=∫−2sin⁡(x)3tdtF′(x)= \begin{array}{l}F(x)=\int_{-2}^{\sin (x)} 3 t d t \\ F^{\prime}(x)=\end{array}

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Find derivatives of sine and cosine functionsright chevron icon

Full solution

Q. F(x)=∫−2sin⁡(x)3tdtF′(x)= \begin{array}{l}F(x)=\int_{-2}^{\sin (x)} 3 t d t \\ F^{\prime}(x)=\end{array}
  1. Identify Function and Limits: Identify the function inside the integral and the limits of integration. F(x)=∫−2sin⁡(x)3t dtF(x) = \int_{-2}^{\sin(x)} 3t \, dt
  2. Apply Fundamental Theorem: Apply the Fundamental Theorem of Calculus Part 11, which states that if F(x)F(x) is the integral of f(t)f(t) from aa to xx, then F′(x)=f(x)F'(x) = f(x).\newlineF′(x)=3sin⁡(x)F'(x) = 3\sin(x)
  3. Check Differentiation: Check for any mistakes in the differentiation process.\newlineNo mistakes found.

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