## Integrals Quiz-7

Important topics for Maths has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with the day-to-day experiences.

Q1. If

then the value of f(e^(-1)) is
•  1
•  0
•

-1
•   None of these
Solution

Q2.The value of

is
•  e
•  In (1+e)
•  e+In (1+e)
•  e-In (1+e)
Solution

Q3.

and is bounded. If

(where a < 1), then a is equal to
•  2/7

•  1/7
•  14/19

•  9/14

Solution

Q4. Let f be a positive function.Let

•  2
•  k
•  1/2
•  1
Solution

Q5.∫sin^(-1) (2x/(1+x^2 ))dx is equal to

•  None of these
Solution
I=∫sin^(-1)⁡(2x/(1+x^2 )) dx, let x=tan⁡Î¸⇒dx=sec^2⁡Î¸ dÎ¸⇒I=∫sin^(-1)⁡((2 tan⁡Î¸)/(1+tan^2⁡Î¸ ))sec^2⁡Î¸dÎ¸ =2∫Î¸ sec^2Î¸ d Î¸ =2(Î¸ tan⁡Î¸-ln⁡|sec⁡Î¸ |)+C =2(x tan^(-1)⁡x-ln⁡|sec⁡(tan^(-1)⁡x )|)+C

Q6. If I(m,n)=

then the expression for I(m,n) in terms of I(m+1,n+1) is
•

•

•

•

Solution

Q7.

If

•  Ï€/60
•  Ï€/20
•  Ï€/40
•  Ï€/80
Solution
Putting a=2,b=3,c=0, we get ∫0^∞dx/((x^2+ 4) (x^2+ 9))=Ï€/(2(2+3)(3+0)(0+2))=Ï€/60

Q8. Given a function f:[0,4]→R is differentiable, then for some

is equals to
•

•

•

•

Solution

Q9.

is equal to
•

•

•

•     None of these
Solution

Q10. The function f and g are positive and continuous. If f is increasing and g is decreasing, then

•  Is always non-positive
•  Is always non-negative
•  Can take positive and negative values
•  None of these
Solution

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Integrals-Quiz 7