Home
Class 12
MATHS
int (0)^(1) (x)/(x^(2)+1)dx...

`int _(0)^(1) (x)/(x^(2)+1)dx`

Text Solution

AI Generated Solution

To solve the integral \( I = \int_{0}^{1} \frac{x}{x^2 + 1} \, dx \), we can use a substitution method. Here’s a step-by-step solution: ### Step 1: Choose a substitution Let \( u = x^2 + 1 \). Then, we need to find \( du \): \[ du = 2x \, dx \quad \Rightarrow \quad \frac{du}{2} = x \, dx \] ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.11|21 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|44 Videos

  • INTEGRATION

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 7.9|22 Videos

  • DIFFERENTIAL EQUATIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|18 Videos

  • INVERES TRIGONOMETRIC FUNCTIONS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise (prove That )|9 Videos

Similar Questions

Explore conceptually related problems

int_(0)^(1) (1)/(x^(2)+x+1)dx

int_(0)^(1) (1)/(1+x+2x^(2))dx

int_(0)^(1) (1)/(x^(2) +2x+3)dx

int_(0)^(1)(2x)/((1+x^(4)))dx

If int_(0)^(1) x e^(x^(2) ) dx=alpha int_(0)^(1) e^(x^(2)) dx , then

If I_(1)=int_(0)^(oo) (dx)/(1+x^(4))dx and I_(2)=underset(0)overset(oo)int x^(2)(dx)/(1+x^(4))"then"n (I_(1))/(I_(2))=

int_(0)^(1)x^2dx

Evaluate: int_(0)^(1)(xe^(x))/(1+x)^(2) dx

If int_(0)^(1) (e^(x))/( 1+x) dx = k , then int_(0)^(1) (e^(x))/( (1+x)^(2)) dx is equal to

Let I= int_(0)^(1) (e^(x))/( x+1) dx, then the vlaue of the intergral int_(0)^(1) (xe^(x^(2)))/( x^(2)+1) dx, is