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Evaluate : (i) int(-oo)^(oo) (dx)/(x^(...

Evaluate :
(i) `int_(-oo)^(oo) (dx)/(x^(2)+2x+2)` , (ii) `int_(sqrt(2))^(oo)(dx)/(xsqrt(x^(2)-1))`, (iii) `int_(0)^(4)(x^(2))/(1+x)dx`
(iv) `int_(0)^(pi//2) sqrt(costheta)sin^(3)theta`

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Verified by Experts

The correct Answer is:
(i) `pi` , (ii) `pi/4` , (iii) `4 + ln 5` , (iv) `8/21`
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 1
  1. Evaluate : (i) int(0)^(1)(3sqrt(x^(2))-4sqrt(x))/(sqrt(x))dx , (ii) ...

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  2. Evaluate : (i) int(-oo)^(oo) (dx)/(x^(2)+2x+2) , (ii) int(sqrt(2))^(...

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  3. Evaluate : (i) int(0)^(1)sin^(-1)xdx , (ii) int(1)^(2)(lnx)/(x^(2))d...

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  4. Evaluate : (i) int(0)^(1)sin^(-1)xdx , (ii) int(1)^(2)(lnx)/(x^(2))d...

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  5. Evaluate : (i) int(0)^(1) (xtan^(-1)x)/((1+x^(2))^(3//2))dx

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  6. Evaluate : (ii) int(0)^(1) (x)/(1+sqrt(x))dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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