Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Need clarity, kindly explain! - Integral Calculus - JEE Main

\int_{0}^{\sqrt{2}}\left [ x^{2} \right ]dx\; is

  • Option 1)

    2-\sqrt{2}\;

  • Option 2)

    \; \; 2+\sqrt{2}\; \; \; \;

  • Option 3)

    \sqrt{2}-1\; \;

  • Option 4)

    \; \sqrt{2}-2\;

 

Answers (1)

best_answer

 

Fundamental Properties of Definite integration -

If the function is continuous in (a, b ) then integration of a function a to b will be same as the sum of integrals of the same function from a to c and c to b.

\int_{b}^{a}f\left ( x \right )dx= \int_{a}^{c}f\left ( x \right )dx+\int_{c}^{b}f\left ( x \right )dx
 

- wherein

 

 

 

\int_{0}^{2}[x^{2}]dx

= \int_{0}^{1}[x^{2}]dx + \int_{0}^{\sqrt{2}}[x^{2}]dx

=\int_{0}^{1}0\ dx + \int_{0}^21\ dx=(\sqrt{2}-1) 


Option 1)

2-\sqrt{2}\;

This is incorrect option

Option 2)

\; \; 2+\sqrt{2}\; \; \; \;

This is incorrect option

Option 3)

\sqrt{2}-1\; \;

This is correct option

Option 4)

\; \sqrt{2}-2\;

This is incorrect option

Posted by

divya.saini

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 Topper: Farmer’s son Gajare Nilkrishna says ‘keep questioning until you understand’
anam-khan

NIT Puducherry Cut-off 2024: Computer Science and Engineering had highest closing rank last year
anam-khan

JEE Mains: Farmer's son from remote Maharashtra village aces exam

Latest Question