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

Evaluate the iterated integral :

01030sin1x(x+y)dzdydx

Short Answer

Expert verified

21π892

Step by step solution

01

Step 1. Given information.

Given integral is :

01030sin1x(x+y)dzdydx

We have to evaluate it.

02

Step 2. Evaluate.

01030sin1x(x+y)dzdydx

=01030sin1x(x+y)dzdydx=0103(x+y)0sin1xdzdydx=0103(x+y)[z]0sin1xdydx=0103(x+y)sin1xdydx

03

Step 3. Integrate with respect to y.

Integrate with respect to y

=0103(x+y)sin1xdydx=01xsin1x03dy+sin1x03ydydx=01xsin1x[y]03+sin1xy2203dx=01xsin1x[3]+sin1x322dx=301xsin1xdx+9201sin1xdx

Use integration by parts :

=3π8+92π21=3π8+9π492=21π892

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