Home
Class 12
MATHS
If In = int sin^n x dx then nIn - (n - 1...

If `I_n = int sin^n x dx then nI_n - (n - 1)I_(n-2) = f(x)+c` where f(x) =

Text Solution

Verified by Experts

The correct Answer is:
`(tan^6x)/6 - I_5+c`
Promotional Banner

Topper's Solved these Questions

  • INDEFINITE INTEGRAL

    PATHFINDER|Exercise QUESTION BANK|39 Videos

  • MATRICES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

If I_n=int( lnx)^n dx then I_n+nI_(n-1)

If I_(n)=int sin^(n)x dx , show that, I_(n)=-(1)/(n) sin^(n-1)x cosx+(n-1)/(n).I_(n-2) . Hence, evaluate, int sin^(6)x dx .

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 (logx)^(n)dx , then the value of (I_(n)+nI_(n-1)) is -

If I_(m,n) = int cos^m x cdot cos nx cdot dx show that (m + n) I_(m,n) = cos^m x cdot sin nx + m I_(m - 1, n-1)

If I_(n)=int cos^(n)x dx , prove that, I_(n)=(1)/(n)cos^(n-1)x sin x+(n-1)/(n).I_(n-2) .Hence, evaluate, int cos^(5)x dx .

Let I_n=int tan^n x dx, (n>1) . If I_4+I_6=a tan^5 x + bx^5 + C , Where C is a constant of integration, then the ordered pair (a,b) is equal to :

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2

sin (n +1) x sin (n +2) x + cos (n +1) x cos (n +2) x = cos x

suppose for every integer n, int_n^(n+1)f(x)dx=n^2 then the value of int_(-2)^4 f(x)dx is