Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Show by differentiating (and then using algebra) that cotsin1xand 1x2xare both antiderivatives of 1x21x2. How can these two very different-looking functions be an antiderivative of the same function?

Short Answer

Expert verified

Ans: By differentiating (and then using algebra) cotsin1xand1x2x both are antiderivatives of 1x21x2

Step by step solution

01

Step 1. Given information.

given expresiion,

cotsin1xand1x2x

02

Step 2. The objective is to show that −cot⁡sin−1⁡x is antiderivatives of 1x21−x2

The differentiation is,

cotsin1x=ddxcotsin1x=cotddxsin1x=cot11x2=1x21x2

Hence the expression is proved.

03

Step 3. The objective is to show that −cot⁡sin−1⁡x is antiderivatives of 1x21−x2

The differentiation is,

1x2x=1x2x=1x2x=1x2x2+1xx2+1x=1x21x2

Hence the expression is proved.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

See all solutions

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free