   Chapter 4.4, Problem 73E

Chapter
Section
Textbook Problem

Finding and Checking an Integral In Exercises 69-74, (a) integrate to find F as a function of x, and (b) demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a). F ( x ) = ∫ π / 4 x sec 2 t   d t

(a)

To determine

To calculate: The value of F(x)=π4xsec2tdt as a function x.

Explanation

Given:

The function, F(x)=π4xsec2tdt

Formula used:

The integration will be broken to parts according to

abf(x)dx=[g(x)]ab.

Also, xndx=xn+1n+1 and sec2xdx=tanx

(b)

To determine

To calculate: The value of obtained function F(x)=tanx1 on differentiation with respect to x.

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