## Integrals Quiz-3

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 Î» is equal to

•  1
•  2
•  3
•  4
Solution

Q2.If Î±,Î² (Î²>Î±) are the roots of g(x)=ax^2+bx+c=0 and f(x) is an even function, then

•  |b/2a|
•  √(b^2-4ac)/(|2a|)
•  |b/a|
•  None of these
Solution

Q3.

is equal to
•

•

•

•

Solution
Putting x tan⁡Î¸=z sin⁡Î¸ ⇒ dx=cos⁡Î¸dz   ⇒ I=cos⁡Î¸ ∫_tan⁡Î¸^1f(z sin⁡Î¸)dz  =-cos⁡Î¸ ∫_1^tan⁡Î¸f(x sin⁡Î¸)dx

Q4. The range of the function f(x)=

•  [-Ï€/2,Ï€/2]
•  [0,Ï€]
•  {0,Ï€}
•  {-Ï€/2,Ï€/2}
Solution

Q5.

If x=

then dy/dx is equal to
•  tan⁡t/2t
•  tan⁡t/t^2
•  tan⁡t/(2t^2 )
•  tan⁡t^2 /(2t^2 )
Solution
dx/dt=sin^(-1)⁡(sin⁡t)cos⁡t=t cos⁡t and dy/dt=sin⁡t/√t∙1/(2√t)=sin⁡t/2t⇒dy/dx=sin⁡t/(2t.t cos⁡t )=tan⁡t/(2t^2 )

Q6. f(x) is a continuous function for all real values of x and satisfies

•  19/2
•  35/2
• 17/2
•  None of these
Solution

Q7.  If I=∫√((5-x)/(2+x)) dx,then I equals
•  √(x+2) √(5-x)+3sin ^(-1) √((x+2)/3)+C
•  √(x+2) √(5-x)+7sin ^(-1) √((x+2)/7)+C
•  √(x+2) √(5-x)+5sin ^(-1) √((x+2)/5)+C
•  None of these
Solution
Put 2+x=t^2, so that dx=2t dt and I=∫√(7-t^2 )/t (2t) dt 2∫√(7-t^2 ) dt=t√(7-t^2 )+7sin^(-1)⁡(t/√7)+C=√(x+2) √(5-x)+7sin^(-1)⁡(√(x+2)/√7)+C

Q8. Given

then the values of K and L are
•  1/(1-m),1/m
•  (1-m),1/m
•  1/(1-m),(m(m-2))/(m-1)
•  m/(m-1),m-2
Solution

Q9.Let f(x)=

and g be the inverse of f. Then the value of g^' (0) is

•  1
•  17
•  √17
•  None of these
Solution

Q10. The value of

where a>1,where[x] denotes the greatest integer not exceeding x is

•  af(a)-{f(1)+f(2)+⋯+f([a] )}
•  [a]f(a)-{f(1)+f(2)+⋯+f([a] )}
•  [a]f([a] )-{f(1)+f(2)+⋯+fA}
• af([a])-{f(1)+f(2)+⋯+fA}
Solution

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Integrals-Quiz 3