Question

5.3 Q4

Answer 1

The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is; g'(x) = √2 ln(t) dt = 1.

What is the derivative of the function g(x) by virtue of the Fundamental theorem of calculus as given in the task content?

g(x) = Integral; √2 ln(t) dt (with the upper and lower limits e^x and 1 respectively).

Since, it follows from the Fundamental theorem of calculus that given an integral where;

Now, g(x) = Integral f(t) dt with limits a and x, it follows that the differential of g(x);

g'(x) = f(x).

Consequently, the function g'(x) which is to be evaluated in this scenario can be determined as:

g'(x) = $\int\limits^{e^x}_1 2 ln(t) dt$ = 1

The derivative of the function g(x) as given in the task content by virtue of the Fundamental theorem of calculus is; g'(x) = √2 ln(t) dt = 1.

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