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If int0^ooe^(-x^2) dx=(sqrtpi)/2 , then...

If `int_0^ooe^(-x^2) dx=(sqrtpi)/2 `, then `int_0^ooe^(-ax^2) dx ` where ` a gt 0` is: (A) `(sqrtpi)/2` (B) `(sqrtpi)/(2a)` (C) `2(sqrtpi)/a` (D) `1/2(sqrt(pi/a))`

A

`(sqrt(2))/(2)`

B

`(sqrt(pi))/(2a)`

C

`2(sqrt(pi))/(a)`

D

`1/2sqrt((pi)/(a))`

Text Solution

Verified by Experts

The correct Answer is:
D
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RESONANCE-DEFINITE INTEGRATION & ITS APPLICATION -Exercise 2 Part - 1
  1. lim(trarr(pi/2)^(-))int(0)^(t) tanthetasqrt(costheta)ln(costheta)d the...

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  2. If f(x) = {{:(0,",""where" x = (n)/(n+1) n = 1"," 2"," 3"......"),(1,...

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  3. If int0^ooe^(-x^2) dx=(sqrtpi)/2 , then int0^ooe^(-ax^2) dx where ...

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  4. If sum(i=1)^(4)(sin^(-1)x(i)+cos^(-1)y(i)) = 6 pi, then sum(i=1)^(4)x...

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  5. The tangent, represented by the graph of the function y=f(x), at the p...

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  6. Let A = int(0)^(1)(e^(t))/(1+t) dt, then int(a-1)^(a)(e^(-1))/(t-a-1) ...

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  7. int1^2 x^(2x^2+1)(1+2lnx)dx is equal to

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  8. If f(x) is a function satifying f(1/x) + x^(2)f(x) = 0 for all non-ze...

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  9. If C0/1+C1/2+C2/3=0 , where C0 C1, C2 are all real, the equation C2x...

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  10. If f(x) = int(0)^(x)(2cos^(2)3t+3sin^(2)3t)dt, f(x+pi) is equal to :

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  11. Let f(x) = int(0)^(x)(dt)/(sqrt(1+t^(2))) and g(x) be the inverse of ...

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  12. Let f(x) is differentiable function satisfying 2int(1)^(2)f(tx) dt ...

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  13. Let I(n) = int(0)^(1)x^(n)(tan^(1)x)dx, n in N, then

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  14. If u(n) = int(0)^(pi//2) x^(n)sinxdx, then the value of u(10) + 90 u(...

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  15. The value of int(1//e)^(tanx)(t)/(1+t^(2))dt+int(1//e)^(cotx)(1)/(t(1+...

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  16. Let A(1) = int(0)^(x)(int(0)^(u)f(t)dt) dt and A(2) = int(0)^(x)f(u).(...

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  17. lim(nrarroo) (sin'(pi)/(2n).sin'(2pi)/(2n).sin'(3pi)/(2n)"......."sin'...

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  18. Area bounded by the region consisting of points (x,y) satisfying y le ...

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  19. Find the area enclosed between the curves: y = loge (x + e) , x = loge...

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  20. The area bounded by the curve x = a cos^3t,, y = a sin^3t, is :

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