Question

calculate the derivative. (use symbolic notation and fractions where needed.)

$$\frac{d}{d t} \int_{100}^{t} \sec (2 x-7) d x=$$

Explanation:

Step1: Apply the Fundamental Theorem of Calculus

If \(F(t)=\int_{a}^{t}f(x)dx\), then \(F^\prime(t) = f(t)\). Here \(a = 100\) and \(f(x)=\sec(2x - 7)\).

Step2: Substitute \(x=t\) into \(f(x)\)

When we apply the theorem, we substitute \(x\) with \(t\) in the function \(f(x)\). So \(f(t)=\sec(2t - 7)\).

Answer:

\(\sec(2t - 7)\)