Question

integrate 1/1+x² under limit 0 and 1​

Answer 1

Answer:

Ok Good Question

Step-by-step explanation:

SOLUTION

TO INTEGRATE

$\displaystyle \sf{ \int\limits_{0}^{1} \frac{1}{1 + {x}^{2} } \, dx }$

EVALUATION

PROCESS 1 :

$\displaystyle \sf{ \int\limits_{0}^{1} \frac{1}{1 + {x}^{2} } \, dx }</p><p>= \displaystyle \sf{{ \tan}^{ - 1} x \: \bigg|_0^1 }</p><p>= \displaystyle \sf{ \frac{\pi}{4} - 0}$

PROCESS 2 : ( USING INDEFINITE INTERGAL )

$\displaystyle \sf{ \int\limits_{0}^{1} \frac{1}{1 + {x}^{2} } \, dx }$

Where C is Integration Constant

Here

$= \displaystyle \sf{ \frac{\pi}{4}}</p><p>\displaystyle \sf{ \int\frac{1}{1 + {x}^{2} } \, dx }</p><p>Where C is integration constant</p><p>Hence</p><p>\displaystyle \sf{ \int\limits_{0}^{1} \frac{1}{1 + {x}^{2} } \, dx }</p><p>= \displaystyle \sf{{ \tan}^{ - 1} x + c \: \bigg|_0^1 }</p><p>= \displaystyle \sf{ \frac{\pi}{4} - 0 + 0}$