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T h ev a l u eofint(sqrt(1n2))^(sqrt(1n3...

`T h ev a l u eofint_(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^2))dxi s` `1/4 1n3/2` (b) `1/21n3/2` `1n3/2` (d) `1/61n3/2`

A

`1/4 ln' 3/2`

B

`1/2 ln' 3/2`

C

`ln'3/2`

D

`1/6 ln' 3/2`

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The correct Answer is:
A
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - I
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  2. Consider the polynomial f(x)= 1+2x+3x^2+4x^3. Let s be the sum of all ...

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  3. T h ev a l u eofint(sqrt(1n2))^(sqrt(1n3))(xsinx^2)/(sinx^2+sin(1n6-x^...

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  4. Let the straight line x= b divide the area enclosed by y=(1-x)^(2),y=0...

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

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  6. Let S be the area of the region enclosed by y-e^(-x^(2)),y=0, x=0 and ...

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  7. The value of the integral int(-pi//2)^(pi//2) (x^(2) + log" (pi-x)/(pi...

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  8. 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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  9. 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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  10. 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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  11. The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the ...

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  12. Let f:[1/2,1]vecR (the set of all real numbers) be a positive, non-con...

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  13. For a epsilonR (the set of all real numbers) a!=-1, lim(n to oo) ((1^(...

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  14. Let f:[a,b]to[1,oo) be a continuous function and let g:RtoR be defined...

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  15. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

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  16. The value of int0^1 4x^3{(d^2)/(dx^2)(1-x^2)^5}dx is

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  17. The following integral int(pi//4)^(pi//2)(2cosec x)^(17) dx dx is equa...

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  18. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  19. Given that for each a epsilon(0,1),lim(hto 0^(+)) int(h)^(1-h)t^(-a)(1...

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  20. ((int(-1/2)^(1/2)cos 2x *log((1+x)/(1-x))dx))/((int(0)^(1/2)cos 2x *lo...

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