Skip to content
## What is the integration of \[ \int_0^1 {\frac{x}{{\sqrt {1 + {x^2}} }}} dx\] ~~~~~[NCERT Exemp. Q. 32,Page 165 ]

# Let \[I = \int_0^1 {\frac{x}{{\sqrt {1 + {x^2}} }}} dx\]

Let’s put \[ 1 + {x^2} = {t^2}\]

# \[ \Rightarrow \] \[2xdx = 2tdt\]

# \[ \Rightarrow \] \[ xdx = tdt\]

# therefore,\[ I = \int_1^{\sqrt 2 } {\frac{{tdt}}{t}} \]

# \[ = [t]_1^{\sqrt 2 } = \sqrt 2 – 1\]

Buy Best Mathematics E-Books Visit : https://mathstudy.in/

## Buy Mathematics Formula Book for Class XI,XII,JEE and other Engineering Competition Exam https://mathstudy.in/product/mathematics-formula-book/

## Buy Mathematics Workbook for Class XII ( Fully Solved ) : https://mathstudy.in/product/work-book-class-xii-c-b-s-e-fully-solved/

## Buy Mathematics Chapter Tests for Class XII ( Fully Solved) : https://mathstudy.in/product/mathematics-chapter-tests-class-xii-c-b-s-e/

## Buy Objective Type Question Bank Class XII (Fully Solved ) : https://mathstudy.in/product/objective-type-question-bank-for-mathematics-class-xii-c-b-s-e/

Let’s put \[ 1 + {x^2} = {t^2}\]

Buy Best Mathematics E-Books Visit : https://mathstudy.in/