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Social Scienceabuate3 dar.valuateVTIV.FTC (part one)Use the fundamental theorem of calculus to write an expression for the anti-derivative of the function y = f(x) = sin(13).If F(x)12 V t+ldt, find the derivative F'(x).Use the fundamental theorem of calculus to find the derivative of the functiony = g(x)-j" cos(t2) dt.Exercise 11 in section 4.4
I am studying for a quiz and do not understand a few of the concepts that will be covered on it. Can you help me with the problem under "IV. FTC (part one)" found in the attached document? Thank you.
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abuate3 dar. valuate VT IV. FTC (part one) Use the fundamental theorem of calculus to write an expression for the anti- derivative of the function y = f(x) = sin(13). If F(x) 12 V t +ldt, find the derivative F'(x). Use the fundamental theorem of calculus to find the derivative of the function y = g(x)-j" cos(t2) dt. Exercise 11 in section 4.4
Expert Answer
The fundamental theorem of calculus states that for a continuous real-valued function, f on a closed interval [a, b], let the function F be defined, for all x in [a, b] as
Here, the function is given as y=sin(x3) which is continuous on any closed interval, hence consider a closed interval [a,b]. Use the fundamental theorem of calculus and obtain the antiderivative F as follows.
The antiderivative F which is uniformly c...
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