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Let f(x) = ln ((1-sinx)/(1+sinx)), then...

Let `f(x) = ln ((1-sinx)/(1+sinx))`, then show that `int_(a)^(b) f(x)dx = int_(b)^(a) ln((1+sinx)/(1-sinx))dx`.

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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1
  1. Evaluate : (ii) int(0)^(1) (x)/(1+sqrt(x))dx

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  2. Evaluate : (i) Find the value a such int(0)^(a)(1)/(e^(x)+4e^(x)+5)d...

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  3. Let f(x) = ln ((1-sinx)/(1+sinx)), then show that int(a)^(b) f(x)dx =...

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  4. Evaluate : (i) int(0)^(2)[x]^(2) dx (where [*] denotes greatest in...

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  5. Evaluate : (i) int(-pi//2)^(pi//2)(g(x)-g(-x))/(f(-x)+f(x))

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  6. Evaluate : (i) int(0)^(2pi) {sin(sinx)+sin(cosx)}dx

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  7. Evaluate : (i) int(0)^(2pi) {sin(sinx)+sin(cosx)}dx

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

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

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

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

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

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

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

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

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

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

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

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

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