Answer :
Final answer:
The question employs the fundamental theorem of calculus-ii to find the derivative of a given function. By applying this theorem, the derivative of the function is determined to be 10x^6, corresponding to option 1).
Explanation:
The question asks for the derivative of the function g(x)=\(\int{2}^{x}(10t^6)dt\) using the fundamental theorem of calculus-ii. According to the fundamental theorem of calculus, if g(x) is defined as the integral of f(t) from a constant to x, then the derivative of g(x), g'(x), is just f(x). Therefore, applying this principle to our function, we replace the variable t in the integral with x to find g'(x) = 10x^6.
