Home
Class 12
MATHS
In = int0^(pi/4) tan^n x dx , then the v...

`I_n = int_0^(pi/4) tan^n` x dx , then the value of `n(l_(n-1) + I_(n+1))` is

Text Solution

AI Generated Solution

To solve the problem, we need to evaluate the integral \( I_n = \int_0^{\frac{\pi}{4}} \tan^n x \, dx \) and find the value of \( n(I_{n-1} + I_{n+1}) \). ### Step-by-Step Solution: 1. **Define the Integral**: \[ I_n = \int_0^{\frac{\pi}{4}} \tan^n x \, dx \] ...
Promotional Banner

Topper's Solved these Questions

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Competition level Questions|80 Videos

  • INTEGRALS

    AAKASH INSTITUTE ENGLISH|Exercise Objective Type Questions (Only one answer)|70 Videos

  • DIFFERENTIAL EQUATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section - J (Aakash Challengers Questions)|4 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    AAKASH INSTITUTE ENGLISH|Exercise ASSIGNMENT (SECTION - J)(ANKASH CHALLENGERS QUESTIONS)|4 Videos

Similar Questions

Explore conceptually related problems

If I_(n)=int_(0)^(pi)x^(n)sinxdx , then find the value of I_(5)+20I_(3) .

If I _(n)=int _(0)^(pi) (sin (2nx))/(sin 2x)dx, then the value of I _( n +(1)/(2)) is equal to (n in I) :

Consider the integral I_(n)=int_(0)^((n)/(4))(sin(2n-1)x)/(sinx)dx , then the value of I_(20)-I_(19) is

If I_(n)=int_(0)^(pi/2) sin^(n)x dx , then show that I_(n)=((n-1)n)I_(n-2) . Hence prove that I_(n)={(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(1/2)(pi)/2,"if",n"is even"),(((n-1)/n)((n-3)/(n-2))((n-5)/(n-4))………(2/3)1,"if",n"is odd"):}

If I_(n)=int_(0)^(2)(2dx)/((1-x^(n))) , then the value of lim_(nrarroo)I_(n) is equal to

Let I_(n) =int _(1) ^(e^(2))(ln x)^(n) dx (x ^(2)), then the value of 3I_(n)+nI_(n-1) equals to:

If I_n=int_0^(pi//4)tan^("n")x dx , prove that I_n+I_(n-2)=1/(n-1)dot

l_(n)=int_(0)^(pi//4)tan^(n)xdx , then lim_(nto oo)n[l_(n)+l_(n-2)] equals

If l_(n)=int_(0)^(pi//4) tan^(n)x dx, n in N "then" I_(n+2)+I_(n) equals

Let I_(n)=int_(0)^(pi//2)(sinx+cosx)^(n)dx(nge2) . Then the value of n. I_(n)-2(n-1)I_(n-1) is