Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • The difference rule of integration <img alt="\int \left [ f\left ( x \right )-g\left ( x \right ) \right ]dx" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cint%20%5Cleft%20%5B%20f%5C

The difference rule of integration \int \left [ f\left ( x \right )-g\left ( x \right ) \right ]dx is

Option: 1

\int f\left ( x \right )dx+\int g\left ( x \right )dx


Option: 2

\int g\left ( x \right )dx-\int f\left ( x \right )dx


Option: 3

-\int f\left ( x \right )dx-\int g\left ( x \right )dx


Option: 4

\int f\left ( x \right )dx-\int g\left ( x \right )dx


Answers (1)

best_answer

Using property (I),

\frac{d}{dx}\left [\int \left [ f\left ( x \right )-g\left ( x \right ) \right ]dx \right ]=f\left ( x \right )-g\left ( x \right )

Using property (II),

\frac{d}{dx}\left [\int f\left (x \right)dx-\int g\left( x \right )dx \right ]=\frac{d}{dx}\int\ f\left ( x \right )dx-\frac{d}{dx}\int\ g\left ( x \right )dx
\frac{d}{dx}\left [\int f\left (x \right)dx-\int g\left( x \right )dx \right ]=f\left ( x \right )-g\left ( x \right )

From the above property, we get,

\int \left [ f\left ( x \right )-g\left ( x \right ) \right ]dx=\int f\left ( x \right )dx-\int g\left ( x \right )dx

Posted by

Ajit Kumar Dubey

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 Marks vs Percentile 2025: How many marks do you need to score 95+ percentile?
anam-khan

JEE Main 2025 session 1 official answer key out; challenge by February 6; how to calculate NTA score?
anam-khan

JEE Main 2025: NIT Raipur's CSE cut-offs drop; closing ranks in popular branches

Latest Question