Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19. Integral 0 to 4 |x - 1 |dx

By using the properties of definite integrals, evaluate the integrals in Exercises 1 to 19.

    Q18.    \int_0^4 |x-1|dx

Answers (1)

best_answer

We have,                          I\ =\ \int_{0}^4|x-1|dx

For opening the modulus we need to define the bracket :

           If     (x - 1)  < 0    then  x belongs to (0, 1).  And if (x - 1) > 0 then x belongs to (1, 4).

So the integral becomes:-              

                                         I\ =\ \int_{0}^{1} -(x-1)dx\ +\ \int_{1}^{4} (x-1)dx

or                                     I\ =\ \left [ x\ -\ \frac{x^2}{2}\ \right ]^{1} _{0}\ +\ \left [ \frac{x^2}{2}\ -\ x \right ]^{4} _{1}

This gives                       I\ =\ 5 

Posted by

Devendra Khairwa

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 10, 12 results 2024 likely after May 20, says result portal
anam-khan

CBSE Result Date 2024 Live: CBSE Class 10, 12 board results for 39 lakh students at cbse.nic.in after May 20
anam-khan

CBSE Results 2024: Last 9 years’ CBSE Class 10, 12 result date and time; links to check score

Latest Question