   Chapter 4.4, Problem 75E

Chapter
Section
Textbook Problem

Using the Second Fundamental Theorem of Calculus In Exercises 75-80, use the Second Fundamental Theorem of Calculus to find F'( x ). F ( x ) = ∫ − 2 x ( t 2 − 2 t )   d t

To determine

To calculate: The value of function F(x)=2x(t22t)dt on differentiation using second fundamental theorem of calculus.

Explanation

Given:

The function,

F(x)=2x(t22t)dt

Formula used:

The differentiation will be broken to parts according to

Using formula

ddx(f(x)+g(x))=ddx(f(x))+ddx(g(x))

According to the second fundamental of calculus, where u is the upper limit in the integral.

ddx[axf(t)dt]=f(x)

Calculation:

On considering the given integral

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