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If I(n) = int(-x)^(x) (sinnx)/((1+pi^(x)...

If `I_(n) = int_(-x)^(x) (sinnx)/((1+pi^(x))sinx)dx, n = 0,1,2"…….."`, then

A

`I_(n) = I_(n+2)`

B

`underset(m=1)overset(10)sumI_(2m+1) = 10 pi`

C

`underset(m=1)overset(10)sum I_(2m) = 0`

D

`I_(n) = I_(n+1)`

Text Solution

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The correct Answer is:
A, B, C
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
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  2. Let f : R rarr R be a continuous function function which satisfies f(x...

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  3. The area of the region bounded by the curve y=e^x and lines x=0a n dy=...

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  6. Let f be a real-valued function defined on the interval (0,oo) by f(x)...

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  7. For any real number, let [x] denotes the largest integer less than or ...

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  8. Let f be a real-valued function defined on the interval (-1,1) such th...

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  9. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

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  10. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

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  11. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

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  12. The value of int(sqrt(ln2))^(ln3)(xsinx^(2))/(sinx^(2)+sin(ln6-x^(2)))...

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  13. Let the straight line x = b divide the area enclosed by y = (1-x)^(2),...

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  14. Let f : [-1,2]rarr[0,oo) be a continuous function such that f(x) = f(1...

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  15. Let S be the area of the region enclosed by y=e^-x^2,y=0,x=0,a n dx=1....

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  16. The value of the integral int(-pi//2)^(pi//2) (x^(2)+ln'(pi+x)/(x-a)) ...

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  17. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

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  18. Let f(x) = (1-x)^(2) sin^(2)x+ x^(2) for all x in IR and let g(x) = in...

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  19. If f(x) = int(0)^(x) e^(t^(2)) (t-2) (t-3) dt for all x in (0, oo) , t...

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  20. The area enclosed by the curvesy= sinx+cosx and y = | cosx-sin x | ove...

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