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If y = int(0)^(x) (t^(2))/(sqrt(t^(2)+1)...

If `y = int_(0)^(x) (t^(2))/(sqrt(t^(2)+1))dt` then `(dy)/(dx)` at `x=1` is

A

`sqrt(2)`

B

`1/2`

C

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

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-DEFINITE INTEGRALS-PRACTICE EXERCISE
  1. int(0)^(pi//2) (x sec^(2). x/2 + 2 tan. x/2)dx=

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  2. If f(x) = int(0)^(x) t.e^(t) dt then f'(-1)=

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  3. If y = int(0)^(x) (t^(2))/(sqrt(t^(2)+1))dt then (dy)/(dx) at x=1 is

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  4. If int(0)^(x)f(t)dt=x+int(x)^(1)tf(t)dt, then the value of f(1) is

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  5. Equation of the tangent line to the curve y= int(0)^(x) cos theta d th...

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  6. (d)/(dx) F(x) = (e^(sin x))/(x) , x gt 0. If int(1)^(4) (2e^(sin x^(2)...

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  7. If f(x)=|{:(cosx,1,0),(1,2cosx,1),(0,1,2cosx):}|" then "int(0)^(pi//2)...

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  8. int(0)^((pi)/(2n))(dx)/(1+Cot^(n)nx)=

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  9. By using the properties of definite integrals, evaluate the integrals ...

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  10. If int(0)^(pi//2) ln (sin x) dx= - pi/2 ln 2 then int(0)^(pi) ln (1+ c...

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  11. int(0)^(oo)(log(1+x^(2)))/(1+x^(2))dx=

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  12. int(0)^(1) ln Sin((pi x)/(2))dx=

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  13. If int(0)^(pi//2) sin^(4) x cos^(2)x dx = (pi)/(32) then int(0)^(pi//2...

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  14. int(0)^(pi//2) sin 2 x.ln(tan x)dx

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  15. int(0)^(pi//2) ln ((4+3 Sin x)/(4+3 Cos x))dx=

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  16. int(0)^(1)x(1-x)^(10)dx=

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  17. If f(x) and g(x) are continuous functions satisfysing f(x)=f(a-x)andg(...

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  18. int(0)^(oo) (x)/((1+x)(1+x^(2)))dx=

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  19. int(-1)^(1) (cos h x)/(1+e^(2x))dx=

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  20. Evaluate the definite integrals . underset(-pi//2)overset(pi//2)int ...

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