record: 173 score: 173 if f(x)=∫₂ˣ(sin(t²)+5)dt, then f(x)= sin(x²) 2x cos(x²)+5 sin(x²)+5 2x cos(x²)

Answer:

C. $\sin(x^{2}) + 5$

Explanation:

Step1: Recall the fundamental theorem of calculus

If $F(x)=\int_{a}^{x}g(t)dt$, then $F^{\prime}(x) = g(x)$.

Step2: Identify the function $g(t)$

Here, $g(t)=\sin(t^{2})+5$.

Step3: Apply the theorem

Since $f(x)=\int_{2}^{x}(\sin(t^{2}) + 5)dt$, by the fundamental theorem of calculus, $f^{\prime}(x)=\sin(x^{2})+5$.