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If I(m"," n)=int cos^(m)x*cos nx dx, sho...

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

A

`(cos^(m)xsinnx)/(n)+c`

B

`cos^(m)xsinnx+c`

C

`(cos^(m)xsinnx)/(n)+c`

D

`-cos^(m)xcosnx+c`

Text Solution

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FIITJEE-INDEFINTE INTEGRAL-SOLVED PROBLEMS (OBJECTIVE)
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  2. If I(m"," n)=int cos^(m)x*cos nx dx, show that (m+n)I(m","n)=cos^(m)x*...

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  3. If inte^(ax)cosbx dx=(e2x)/(29)f(x)+C , then f'' (x)=

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  4. int(x+(1)/(x))^(n+5).((x^(2)-1)/(x^(2)))dx is equal to

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  5. If int(cos^(2)x)/(sin^(6)x)dx=Acot^(5)x+Bcot^(3)x+k, then A+B equals

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  6. If f'(x)=x|sinx|AAx""in(0,x)andf(0)=(1)/(sqrt3), then f(x) will be

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  7. int((x^(2)-1))/((x^(2)+1)sqrt(x^(4)+1))dx is equal to

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  8. Evaluate: int(x+x^(2/3)+x^(1/6))/(x(1+x^(1/3))).dx

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  9. If int(e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx=mue^(x)((1+x)/(1-x))^(la...

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  10. int(dx)/(xsqrt(1-x^(3)))dx=

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  11. he value of the integral inte^(sin^(2x))(cosx+cos^3x)sinx dx is

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  12. If int(dx)/(5+4cosx)=ktan^(-1)(mtan""(x)/(2))+c, then

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  13. If intsqrt(cosecx+1)dx,kfog(x)+c, where k is a real constant, then

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  14. If f'(x)=(1)/(-x+sqrt(x^(2)+1))andf(0)=(-(1+sqrt2))/(2), then the valu...

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  15. int(dx)/(root(3)((x-1)^(4)*(x+1)^(2)))

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  16. I=int (dx)/(""^(4)sqrt( (x-1) ^(3) (x+2)^(5)))=k ""^(4)sqrt((x-1)/(x+2...

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  17. For integral int f(x- a/x)*(1+a/x^(2))dx, put x-a/x=t For integral i...

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  18. Evaluate: int(x-1)/((x+1)sqrt(x^3+x^2+x))\ dx

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  19. Statement -1 : Integral of an even function is not always on odd funct...

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  20. If int(lnx)/(x^(3))dx=-(lnx)/(ax^(2))-(1)/(bx^(2))+c then the value of...

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