abuate3 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

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Asked Mar 25, 2019
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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.

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
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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

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Expert Answer

Step 1

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

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Step 2

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.

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Step 3

The antiderivative F which is  uniformly c...

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