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For x in (0,(5pi)/(2)), defined f(x) = i...

For `x in (0,(5pi)/(2))`, defined `f(x) = int_(0)^(x) sqrt(t)sint dt`. Then f has:

A

local maximum at `pi` an d `2pi`.

B

local minimum at `pi` an d `2pi`.

C

local maximum at `pi` and local maximum at `2pi`.

D

local maximum at `pi` and local minimum at `2pi`.

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The correct Answer is:
D
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 3 Part - II
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  2. The area bounded by the curves y=cosx and y=sinx between the ordinates...

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  3. For x in (0,(5pi)/(2)), defined f(x) = int(0)^(x) sqrt(t)sint dt. Then...

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  4. Let [] denote the greatest integet function then the value int0^1.5 x[...

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  5. The area of the region enclosed by the curvesv y=x,x=e,y=1/x and the p...

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  6. The area bounded by the curves y^2=4x and x^2=4y

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  7. The area bounded between the parabola x^(2)=y/4 and x^(2)=9y and the s...

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  8. If g(x) = int(0)^(x) cos dt, then g(x+pi) equals

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  9. Statement-I : The value of the integral int(pi//6)^(pi//3)(dx)/(1+sq...

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  10. The area (in square units) bounded by the curves y=sqrt(x),""2y-x+3=0 ...

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  11. The integral int(0)^(pi)sqrt(1+4sin^(2)'x/2-4sin'x/2)dx equals:

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  12. The area of the region described by A = {(x,y) : x^(2)+y^(2) le 1 and ...

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  13. The integral int(2)^(4) (logx^(3))/(logx^(2)+log(36-12x+x^(2)))dx is e...

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  14. The area (in sq units) of the region described by {(x,y):y^(2)le2x and...

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  15. The area (in sq. units) of the region {(x,y):y^(2) le 2x and x^(2)...

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  16. lim(nrarroo) (((n+1)(n+2)"........"3n)/(n^(2n)))^(1//n) is equal to :

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  17. The area ( in sq. units) of the region {(x,y) : x ge 0, x + y le 3, x...

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  18. The integral int(pi/4)^((3pi)/(4)) (dX)/(1+cosx) is equal to

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  19. The value of int(pi/2)^( pi/2) (sin^(2)x)/(1+2^(x)) dx is :

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  20. Let g(x) = cosx^(2), f(x) = sqrt(x), and alpha, beta (alpha lt beta)...

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