. In this question you will adapt two different ways to compute ſsec® de in order compute ſcsc0 d0. Adapting a solution you've seen to solve a new problem is an important skill in mathematics; it means that instead of just solving one problem, you can solve many different problems! (1) See p. 483 of the textbook for the most common strategy for integrating sece. Adapt this to compute Scsc0 d0.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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. In this question you will adapt two different ways to compute fsece de in order compute ſcsce do. Adapting a
solution you’ve seen to solve a new problem is an important skill in mathematics; it means that instead of just solving one
problem, you can solve many different problems!
(1) See p. 483 of the textbook for the most common strategy for integrating sece. Adapt this to compute ſcsce de.
The first short computation of the integral of sece is due to Isaac Barrow. Adapt his computations to compute ſcsce de.
You can find his computations on p. 4 of “An Application of Geography to Mathematics: History of the Integral of the
Secant" by Rickey and Tuchinsky.
Transcribed Image Text:. In this question you will adapt two different ways to compute fsece de in order compute ſcsce do. Adapting a solution you’ve seen to solve a new problem is an important skill in mathematics; it means that instead of just solving one problem, you can solve many different problems! (1) See p. 483 of the textbook for the most common strategy for integrating sece. Adapt this to compute ſcsce de. The first short computation of the integral of sece is due to Isaac Barrow. Adapt his computations to compute ſcsce de. You can find his computations on p. 4 of “An Application of Geography to Mathematics: History of the Integral of the Secant" by Rickey and Tuchinsky.
Isaac Barrow (1630–1677) in his Geometrical Lectures (Lect. XII, App. I) gave the first
"intelligible" proof of the result, but it was couched in the geometric idiom of the day. It is
especially noteworthy in that it is the earliest use of partial fractions in integration. Thus we
reproduce it here in modern garb:
1
de
cos e
O do =
cos e
de
-) Cos? 0
cos 0
de
=J1- sin?0
cos e
do
-J (1- sin0)(1+ sin 0)
cos e
1- sin0
cos 0
1+sine
+
do
-In|1-sine|+In|1+sin |]+ c
=
1+ sin0
-n1-sine
1+ sin0 1+sin0
In
1-sin0 1+sin 0
+c
|(1+sin0)²
-n1-sin*o
-In
+c
|(1+sin0)?
In
+c
=
(cos8)?
1+sin0
+ c
= In cose
=In|sec0+ tan 0|+c.
Transcribed Image Text:Isaac Barrow (1630–1677) in his Geometrical Lectures (Lect. XII, App. I) gave the first "intelligible" proof of the result, but it was couched in the geometric idiom of the day. It is especially noteworthy in that it is the earliest use of partial fractions in integration. Thus we reproduce it here in modern garb: 1 de cos e O do = cos e de -) Cos? 0 cos 0 de =J1- sin?0 cos e do -J (1- sin0)(1+ sin 0) cos e 1- sin0 cos 0 1+sine + do -In|1-sine|+In|1+sin |]+ c = 1+ sin0 -n1-sine 1+ sin0 1+sin0 In 1-sin0 1+sin 0 +c |(1+sin0)² -n1-sin*o -In +c |(1+sin0)? In +c = (cos8)? 1+sin0 + c = In cose =In|sec0+ tan 0|+c.
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