Verify the integration formulas in Exercises 37–40.sech x dx = tan'(sinh x) + C37. a.sech x dx = sin-'(tanh x) + Cb.1 - x² + Cx sechx dx =38.-sech¯lxx² – 1-coth¬1,| x cothx dxx ++ C39.tanhx dx = x tanh'x + ;In(1 – x²) + C40.

Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Answered: Verify the integration formulas in…

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...

See similar textbooks

Similar questions

Let u = x3 + 1. Indicate how the limits of integration should be adjusted in order to perform the integration with respect to u. (Enter your answer using interval notation.) (0,2)
Limit _π/2 toπ/2 integral (1+cosx) dx
Find the linearization of ƒ(x) = √(x + 1) + sin x at x = 0. How is it related to the individual linearizations of √(x + 1) and sin x at x = 0?
2. Verify using the Integration (preferably integration by parts if possible) Techniques each of the equalities a and b :
Integral of cos2x on [0, infinity]
Use partial integration to derive that from image without deriving the right side. Here one can consider ∫ tanx dx = ln ∣sec x∣ + C = −ln ∣cosx∣ + C and ∫ tan2 x = tanx − x + C as known integrals
Evaluate integration e^(-3x)cos(3x) dx using integration by parts
Integrate the differential (x^2+y)dx+xdy from (0,0) to (1,1) along two paths: first from (0,0) to (1,0) to (1,1), and then from (0,0) to (0,1) to (1,1). Is the value of the integral the same? Now repeat this exercise with the differential (x^2 + 2y)dx + xdy.
2. Verify using the Integration (preferably integration by parts if possible) Techniques each of the equality
SHOW A C.OMPLETE AND DETAILED SOLUTION; IF AN INTEGRATION FORM.ULA IS USED FROM A TABLE OF INTEGRATION FORMULAS, SHOW DERIVATION FIRST.
Solve using integration of parts: ∫x2 cos x dx
Show that sec x = (sin x / cos x) + (cos x / 1 + sin x), then use the identity to drive the basic integration rule S sec x dx = In I sec x + tan x I + C

SEE MORE QUESTIONS

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Verify the integration formulas in Exercises 37–40. sech x dx = tan'(sinh x) + C 37. a. sech x dx = sin-'(tanh x) + C b. 1 - x² + C x sechx dx = 38. -sech¯lx x² – 1 -coth¬1, | x cothx dx x ++ C 39. tanhx dx = x tanh'x + ;In(1 – x²) + C 40.