Let , where is continuous on its domain. Which of the following is equal to for all…

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

Let

F(x)=\int_{2}^{x} g(t)\,dt

, where

g

is continuous on its domain. Which of the following is equal to

F'(x)

for all

x

in the domain of

g

? (a)

\displaystyle \frac{1}{x-2}\int_{2}^{x} g(t)\,dt

(b)

g(2)

(c)

g(x)

(d)

\displaystyle \int_{2}^{x} g'(t)\,dt