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If In=int0^(pi//4)tan^("n")x dx , pro...

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

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The correct Answer is:
`2/(1+x^(2))[2x^(2)+(1+x^(2))ln(1+x^(2))]`
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Self practive problem
  1. Prove the following inequalities : (i) (sqrt(3))/(8) lt int(pi//4)^(...

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  2. Show that (i) (1)/(10sqrt(2))lt underset(0)overset(1)int(x^(9))/(sq...

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  3. If In=int0^(pi//4)tan^("n")x dx , prove that In+I(n-2)=1/(n+1)dot

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  4. Find the area enclosed betweent the curve y = x^(2)+3, y = 0, x = -...

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  5. int sinx dx

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  6. Find the area of the region bounded by the curve y^2=2y-x and the y-ax...

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  7. Find the area bounded by the y-axis and the curve x = e^(y) sin piy b...

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  8. The area bounded by (x^(2))/(16) + (y^(2))/(9) = 1 and the line 3x + 4...

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  9. Compute the area of the figure bounded by the straight lines x=0,x=2...

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  10. If the area bounded by f(x)=sqrt(tan x), y=f(c), x=0 and x=a, 0ltcltal...

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  11. Find the area included between the parabolas x=y^(2) and x = 3-2y^(2).

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  12. If An be the area bounded by the curve y=(tanx)^n and the lines x=0,\ ...

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  13. If int(1)^(x) (dt)/(|t|sqrt(t^(2)-t)) = (pi)/(6), then x can be equal ...

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  14. The value of the integral int(0)^(1)(dx)/(x^(2)+2x cos alpha +1),0ltal...

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  15. If f(x)={{:(x,xlt1),(x-1,xge1):}, then underset(0)overset(2)intx^(2)f(...

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  16. If f(0) = 1 , f(2) = 3, f'(2) = 5 and f'(0) is finite, then int(0)^(1...

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  17. int(0)^(pi)|1+2cosx| dx is equal to :

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  18. The value of int(1)^(3) (|x-2|+[x])dx is ([x] stands for greatest inte...

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  19. The value of int(0)^(infty)[2e^(-x)] dx (where ,[.] denotes the greate...

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  20. int(lnpi-ln2)^(lnpi) (e^(x))/(1-cos(2/3e^(x))) dx is equal to

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