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

Consider the integral sin2xcos2xdx. We solved this integral in Example 2(b) by applying double-angle identities at the very beginning.

(a) Solve this integral by applying the identity sin2x=1-cos2x

(b) Solve this integral another way, by applying the identitysinxcosx=12sin2x

Short Answer

Expert verified

(a)x8-sin4x32+C

(b)x8-sin4x32+C

Step by step solution

01

Part (a) Step 1. Explanation

sin2xcos2xdx=1-cos2xcos2xdx=cos2x-cos4xdx=12+cos2x2-cos4xdx=x2+sin2x4-cos4xdx=x2+sin2x4-cos2x2+cos4x8+38dx=x2+sin2x4-sin2x4-sin4x32-38x+C=x8-sin4x32+C

02

Part (b) Step 1. Explanation

sin2xcos2xdx=14sin22x=1412-cos4x2dx=x8-sin4x32+C

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

Study anywhere. Anytime. Across all devices.

Sign-up for free