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If int(0)^(y)cost^(2)dt=int(0)^(x^(2))(s...

If `int_(0)^(y)cost^(2)dt=int_(0)^(x^(2))(sint)/tdt`, then prove that `(dy)/(dx)=(2sinx^(2))/(xcosy^(2))`.

A

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

B

`(2sinx^(2))/(xcosy^(2))`

C

`(2sinx)/(x(1-2sin'(y^(2))/(2)))`

D

`(sinx^(2))/(2y)`

Text Solution

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The correct Answer is:
B
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RESONANCE ENGLISH-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1 Part-II
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  2. The value of function f (x) =1 +x+ int (1) ^(x) (ln ^(2)t +2 ln t ) dt...

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  3. If int(0)^(y)cost^(2)dt=int(0)^(x^(2))(sint)/tdt, then prove that (dy)...

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  4. If int(sinx)^(1)t^(2) (f(t)) dt = (1-sinx), then f ((1)/(sqrt(3))) is

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  5. The value of lim(a rarr oo)(1)/(a^(2))int(0)^(a)ln(1+e^(x))dx equals

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  6. int(0)^(pi//2) sin^(4)xcos^(3)dx is equal to :

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  7. int(0)^(1)x^(2)(1-x)^(3)dx is equal to

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  8. Let I = int(1)^(3)sqrt(x^(4)+x^(2)), dx then

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  9. I=int0^(2pi) e^(sin^2x+sinx+1)dx then

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  10. Let f(x) = secx*f'(x), f(0) = 1, then f(pi/6) is equal to

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  11. Let mean value of f(x) = 1/(x+c) over interval (0,2) is 1/2 ln 3 then...

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  12. lim(nrarr0) sum(r=1)^(n) ((r^(3))/(r^(4)+n^(4))) equals to :

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

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  14. 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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  15. lim(nrarroo) [sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))/(n)pi] i...

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  16. Let I(n) = int(0)^(1)(1-x^(3))^(n)dx, (nin N) then

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  17. The area bounded by the x-axis and the curve y = 4x - x^2 - 3 is

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  18. The area of the figure bounded by right of the line y = x + 1, y= cos ...

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  19. Area bounded by curve y^(3) - 9y + x = 0, and y-axis is

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  20. Let f":[0,oo)rarr R be a continuous and stricity increasing function ...

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