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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) =

A

`sin^(n - 1)x cos x`

B

`cos^(n - 1)x sin x`

C

`-sin^(n - 1)x cos x`

D

`-cos^(n - 1)x sin x`

Text Solution

Verified by Experts

The correct Answer is:
C
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PATHFINDER-INDEFINITE INTEGRATION-QUESTION BANK
  1. int [In(Inx) + 1/(Inx)^2]dx is

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  2. If int g(x)dx = g(x) , then int g(x){f(x) - f'(x)}dx is equal to

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  3. If In = int sin^n x dx then nIn - (n - 1)I(n-2) = f(x)+c where f(x) =

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  4. Plot the function f(x)= max{x, x^2, x^3}

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  5. If int dx/(x^4 + x^3) is equal to logabs(x/(x+1)) + 1/x + k/x^2 + c

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  6. int dx/((1+sqrtx)sqrt(x-x^2) is equal to ?

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  7. If int (cos 4x + 1)/(cot x - tan x) dx = A cos 4x + B, then

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  8. If int e^x (tanx - log cos x) dx = f(x) log sec x then range of f(x) i...

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  9. If int (bx cos4x - asin 4x )/x^2 dx = (asin4x)/x + c then a, b may be

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  10. if int (e^(6logx) - e^(4logx))/(e^(3logx)-e^(2logx)) dx = phi(x), then...

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  11. If int dx/(x^6 + x^4) = tan^-1x + 1/x + k/x^3 + c, then value of k is

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  12. int (f(x)phi'(x)-phi(x)f'(x))/(f(x)phi(x)) {logphi(x) - logf(x)} dx is

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  13. int dx/(x^n(1+x^n)^(1/n)) is

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  14. If int dx/((x+1)^3 + (x+1)^2) is k[t - t^2/2 + t^3/3 - Inabst ] +c wh...

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  15. int (cos^3 x + cos^5 x)/(sin^2 x + sin^4 x) dx equals

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  16. int (sec x dx)/([sin(2x+alpha) + sin alpha]^(1/2)) is

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  17. If int (cos^4 x dx)/(sin^3 x (sin^5 x + cos^5 x)^(3/5)) is equal to -1...

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  18. Let f(x) = x + sin x . Suppose 'g' denotes the inverse function of 'f...

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  19. I = int 1/(cos^4 x) dx is equal to

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  20. int (x + 5)/((x-1)^2 (x-2)) dx =

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