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Ifint(-pi)^((3pi)/4)(e^(pi/4)dx)/((e^x+e...

`Ifint_(-pi)^((3pi)/4)(e^(pi/4)dx)/((e^x+e^(pi/4))(sinx+cosx)=kint_(-pi/2)^(pi/2)secx dx ,t h e nt h ev a l u eofki s` `1/2` (b) `1/(sqrt(2))` (c) `1/(2sqrt(2))` (d) `-1/(sqrt(2))`

A

`(1)/(2)`

B

`(1)/(sqrt2)`

C

`(1)/(2sqrt2)`

D

`-(1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
C
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FIITJEE-TIPS-ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)
  1. "I f"I1=int(-100)^(101)(dx)/((5+2x-2x^2)(1+e^(2-4x))) "and"I2=int(-10...

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  2. If f(x)=[|x|], then int0^100 f(x)dx is equal to (where [.] denotes the...

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  3. Ifint(-pi)^((3pi)/4)(e^(pi/4)dx)/((e^x+e^(pi/4))(sinx+cosx)=kint(-pi/2...

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  4. If k be positive integer , then the number of values of k satisfying i...

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  5. If the ordinate x = a divides the area bounded by the curve y=1+(8)/(...

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  6. Area common to the circle x^2+y^2=64 and the parabola y^2=4x is

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  7. The ratio of the areas between the curves y=cos x and y=cos 2x and x-...

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  8. Area bounded by y = |x - pi/2| and x = 0, x = pi equals

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  9. The area cut off a parabola 4y=3x^(2) by the straight line 2y=3x+12 in...

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  10. Find the area of the region lying in the first quadrant and bounded b...

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  11. The area of smaller portion of the circle x^2+y^2=a^2 cut off by the l...

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  12. The area of the smaller portion of the circle x^2+y^2=4 cut off the l...

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  13. The area of the region bounded by y = |x - 1| and y = 1 is

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  14. The area bounded by the parabola y^2 = x, straight line y = 4 and y-ax...

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  15. What is the solution of y'=1+x+y^(2)+xy^(2),y(0)=0?

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  16. The solution of the differential equation ((dy)/(dx))^(2)-x((dy)/(dx))...

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  17. The solution of the differential equation log(dy/dx)=4x-2y-2,y=1 ,wher...

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  18. If y=x/(In|cx|) (where c is an arbitrary constant) is the general solu...

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  19. I .F. for y in y dx/dy + x - ln y=0 is

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  20. Which of the following is a differential equation of the family of cur...

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