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If int0^y cos t^2\ dt = int0^(x^2)\ sint...

If `int_0^y cos t^2\ dt = int_0^(x^2)\ sint/t \ dt`, then `dy/dx` is equal to

A

`(2 sin ^(2) x )/(x cos ^(2) y)`

B

` (2 sin x ^(2))/( x cos y ^(2))`

C

`(2 sin x ^(2))/(x (1- 2 sin ""(y ^(2))/(2)))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
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MOTION-DEFINITE INTEGRATION -EXERCISE -2 (LEVEL-I)
  1. The value of lim(xto0) (int(0)^(x^2)sec^2t dt)/(x sin x) dx , is

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  2. underset( x to 0) lim ( int(0)^(x^(2)) cos^(2)t" "dt)/(x sin x) = ...

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  3. If int0^y cos t^2\ dt = int0^(x^2)\ sint/t \ dt, then dy/dx is equal t...

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  4. let f(x)=int(t^2-t+1)dt,AA x in (3,4), then the difference between th...

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  5. Ifint(sinx)^1t^2f(t)dt=1=1-s inx ,w h e r ex in (0,pi/2), then find t...

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  6. The smallest interval [a,b] such that overset(1)underset(0)int (1)/...

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  7. Given that n is odd and m is even integer. the value of int (0) ^(x ) ...

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  8. underset(n to oo)"lim"underset(r=1)overset(n)sum((r^(3))/(r^(4) + n^(4...

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  9. underset(n to oo)lim" " underset(r=2n+1)overset(3n)sum (n)/(r^(2)-...

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  10. lim(n->oo)[(1+1/n^2)(1+2^2 /n^2)(1+3^2 /n^2)......(1+n^2 / n^2)]^(1/n)

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  11. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  12. Lim(n->oo)[1/n^2 * sec^2 (1/n^2)+2/n^2 * sec^2 (4/n^2)+..............+...

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  13. If int (0)^(x^(2)) f(t) dt = x cos pix , then the value of f(4) is

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  14. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  15. Let I (1) = int (1) ^(2) (dx )/(sqrt(1 + x ^(2))) and I (2) = int (1) ...

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  16. If I(n)=underset(0)overset(pi//4)inttan^(n)x dx, then (1)/(I(2)+I(4)...

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  17. If I (1) = int (0) ^(1) 2 ^(x ^(2)) dx, I (2) = int (0) ^(1) 2 ^(x ^(3...

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  18. If u (n) = int (0) ^(pi//2) x ^(n) sin x dx, n in N then the value of ...

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  19. The vlaue of the integral underset(-1)overset(3 )int ("tan"^(1)(x)/(...

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  20. In = int0^(pi/4) tan^n x dx , then the value of n(l(n-1) + I(n+1)) is

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