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If y = int(1)^(x) xsqrt(lnt)dt then fi...

If `y = int_(1)^(x) xsqrt(lnt)dt`
then find the value of `(d^(2)y)/(dx^(2))` at `x = e`

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The correct Answer is:
`5//2`
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1
  1. Evaluate : (i) int(0)^(2pi) {sin(sinx)+sin(cosx)}dx

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  2. Evaluate : (i) int(-1)^(2){2x}dx (where function{*} denotes fraction...

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  3. If f(x) is a function defined AA x in R and f(x) + f(-x) = 0 AA x in [...

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  4. (i) if f(x) = 5^(g(x)) and g(x) = int(2)^(x^(2))(t)/(ln(1+t^(2))) dt, ...

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  5. The value of overset(sin^(2)x)underset(0)int sin^(-1)sqrt(t)dt+overs...

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  6. If y = int(1)^(x) xsqrt(lnt)dt then find the value of (d^(2)y)/(dx^(...

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  7. lim(n to oo)n^2*int(1/(n+1))^(1/n)(tan^(-1)(nx)/sin^(-1)(nx)dx) is equ...

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  8. Let f be a differentiable function on R and satisfying the integral eq...

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  9. Evaluate : int(0)^(pi)xsin^(5)xdx

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  10. Evaluate : Lim(nrarroo) 3/n[1+sqrt((n)/(n+3))+sqrt((n)/(n+6))+sqrt((n...

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  11. Find the area enclosed betweent the curve y = x^(2)+3, y = 0, x = - 1,...

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  12. (i) Find the area bounded by x^(2)+y^(2)-2x=0 and y = sin'(pix)/(2) in...

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  13. Examples: Find the area of the region bounded by the curve y^2 = 2y - ...

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  14. Find the area bounded by the y-axis and the curve x = e^(y) sin piy, ...

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  15. The smaller area bounded by x^2/16+y^2/9=1 and the line 3x+4y=12 is

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  16. Compute the area of the figure bounded by the straight lines =0,x=2...

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  17. If the area bounded by f(x)=sqrt(tan x), y=f(c), x=0 and x=a, 0ltcltal...

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  18. For the area included between the parabolas x=y^(2) and x = 3-2y^(2).

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  19. A tangent is drawn to the curve x^(2)+2x-4ky+3=0 at a point whose absc...

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  20. If An be the area bounded by the curve y=(tanx^n) ands the lines x=0,\...

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