Integral Calculus MCQ Level - 2 - Physics MCQ

The required area will be  


The correct answer is:  

To find the intersection, eliminating r between the two equations, i.e.,

∴   The required area will be given by,

The correct answer is: 

The required area will be given by

The correct answer is: 1/3 sq.units

The curve is symmetrical about y-axis

Hence, the required area will be,

The correct answer is: πa² sq. units

The required area will be given by

The correct answer is: 

The required area will be given by


The correct answer is:  

The area of the given cardio-id will be given by

The correct answer is:  

The region of integration is enclosed by r = a, r = a(1 + cosθ), 

∴   The required area


The correct answer is: 

To find the point of intersection,
log x = (log x)²
⇒  log x (log x – 1) = 0
⇒  log x = 0        or    log x = 1
⇒  x = 1, e

Hence, the required area will be  

= [e - e - (-1)] - [e - 2e + 2e - 2]
= 1 - (e - 2)
= (3 - e) sq. units

The correct answer is: (3 - e) sq.units

For x ∈ (0, π) y = 1 + sin²x is a non negative, function.
∴ The area bounded. by y = 1 + 2sin²x, x-axis, x = 0 and x = π will be in first quadrant.
∴ The area required  

The correct answer is: 2π sq. units