## Integrals Quiz-5

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∫f(x) sin⁡x cos⁡x dx= 1/2(b^2-a^2 ) ln⁡f(x)+c,then f(x) is equal to

•  1/(a^2 sin^2x+b^2 cos^2 x)
•  1/(a^2 sin^2x-b^2 cos^2 x)
•  1/(a^2 cos^2x+b^2sin^2x)
•  1/(a^2cos^2x-b^2 sin^2x)
Solution
Differentiating, we get (f^' (x))/(f(x)^2 )=2(b^2-a^2 ) sin⁡x cos⁡x Integrating both sides w.r.t. x⇒-1/(f(x))=-b^2 cos^2⁡x-a^2 sin^2⁡x⇒f(x)=1/(a^2 sin^2⁡x+b^2 cos^2⁡x )

Q2.If

then

•

•

•

•  None of these
Solution

Q3.

If S=(1/2)^2+(1/2)^2 1/3+(1/2)^3 1/4+(1/2)^4 1/5+..., then
•  S=In 8-2

•
S=In 4/e

•  S=In 4+1

•  None of these

Solution
Let S =1+x+x^2+ x^3+⋯=1/(1 –x) Integrating w.r.t. x, we get |(x+x^2/2+x^3/3+⋯) |_0^(1/2) =-|In(1–x) |_0^(1/2) ⇒1/2+1/2 (S)=In 2⇒S=In4/e

Q4. If

•  2
•  -3
•  -5
•   None of these
Solution

Q5.

The value of

where x∈(Ï€/6,Ï€/3), is equal to
•  0
•  2
•  1
•  None of these
Solution

Q6. The number of possible continuous f(x) defined in [0,1] for which

•  1
•
• 2
•  0
Solution

Q7.  If

is equal to
•  2e^4-2e-a
•  2e^4-e-a
•  2e^4-e-2a
•  e^4-e-a
Solution

Q8. ∫ln⁡(tan⁡x)/sin⁡xcos⁡x dx is equal to
•  1/2 ln⁡(tan⁡x )+c
•  1/2 ln⁡(tan^2 x)+c
•  1/2 (ln⁡(tan⁡x ) )^2+c
•  None of these
Solution
I=∫ln⁡(tan⁡x)/sin⁡x cos⁡x dx , let t=ln⁡(tan⁡x)⇒dt/dx=sec^2⁡x/tan⁡x ⇒dt=dx/sin⁡x cos⁡x ⇒I=∫tdt=1/2 t^2+C=1/2(ln⁡(tan⁡x))^2+C

Q9.Let f be integrable over [0,a] for any real value of a. If

•

•

•

•

Solution

Q10. The value of the integral

•  3+2Ï€
•  4-Ï€
•  2+Ï€
• None of these
Solution

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BEST NEET COACHING CENTER | BEST IIT JEE COACHING INSTITUTE | BEST NEET & IIT JEE COACHING: Integrals - Quiz 5
Integrals - Quiz 5