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If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2...

If `int_(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int_(0)^(oo) e^(-ax^(2)) dx, a gt0`, s

A

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

B

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

C

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

D

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

Text Solution

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The correct Answer is:
D
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int_(0)^(oo)e^(-x^(2))dx=(sqrtpi)/(2) then

If int_(0)^(oo)e^(-x^(2))dx=(sqrt(pi))/(2), then int_(0)^(oo)e^(-ax^(2))dx where a>0 is: (A)(sqrt(pi))/(2) (B) (sqrt(pi))/(2a)(C)2(sqrt(pi))/(a) (D) (1)/(2)(sqrt((pi)/(a)))

If int_ (0)^(oo) e^(-x^(2)) dx = (sqrt (pi))/(2), and int_ (0)^(oo) e^(-ax^(2) ) dx, a> 0 is (i) (sqrt (pi))/(2) (ii) (sqrt (pi))/(2a) (iii) 2 (sqrt (pi))/(a) (iv) (1)/(2) sqrt ((pi)/(a))

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int_(0)^(oo)(1)/(3+x^(2))dx

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int_(0)^(oo)(a^(-x)-b^(-x))dx

D) int_(0)^(oo)x^(5)e^(-x)dx

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OBJECTIVE RD SHARMA-DEFINITE INTEGRALS-Chapter Test 2
  1. If int(0)^(36) (1)/(2x+9)dx =log k, is equal to

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  2. The value of the integral int(0)^(pi//2) sin^(6) x dx, is

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  3. If int(0)^(oo) e^(-x^(2))dx=sqrt((pi)/(2))"then"int(0)^(oo) e^(-ax^(2)...

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  4. The value of the integral int 0^oo 1/(1+x^4)dx is

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  5. If int(pi//2)^(x) sqrt(3-2sin^(2)u) dx+int(dx)^(dy) equal pi//2

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  6. The value of alpha in [0,2pi] which does not satify the equation int(p...

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  7. lim(x to 0)(int(0)^t(x^(2))sinsqrt(t) dt)/(x^(3)) is equl to

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  8. If x satisfies the equation x^(2)( int(0)^(1) (dt)/(t^(2)+ 2t cos al...

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  9. The value of alpha in (-pi, 0) satisfying sin alpha+int(alpha)^(2alpha...

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  10. The value of int(0)^(pi//2) (sin^(3)x cos x)/(sin^(4)x+ cos^(4)x )dx i...

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  11. The value of int(0)^(pi) (1)/(5+3cosx)dx, is

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  12. underset(nrarroo)"lim"[sin'(pi)/(n)+sin'(2pi)/(n)+"......"+sin'((n-1))...

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  13. lim(n to oo) sum(r=1)^(n) {(r^(3))/(r^(4)+n^(4))} equals

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  14. lim(n-gtoo)[(1+1/n)(1+2/n)(1+n/n)]^(1/n)

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  15. Evaluate: (lim)(nvecoo)n[1/(n a)+1/(n a+1)+1/(n a+2)++1/(n b)]

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  16. The solution of the equation int(0)^(x) (1)/(xsqrt(2^(2)-1))dx=(pi)/(1...

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  17. Let I(n)=int(0)^(pi//4) tan^(n) x dx, (n gt1 and n in N), then

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  18. If I(m)=int(1)^(x) (log x)^(m)dx satisfies the relation Im = k-lI(m-1...

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  19. If I(m)=int(0)^(oo) e^(-x)x^(n-1)dx, "then" int(0)^(oo) e^(-lambdax) x...

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  20. If I(m,n)=int(0)^(1)x^(m-1) (1-x)^(n-1)dx then

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