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Integral Calculus MCQ Level - 2 Physics MCQs & solutions - Free


MCQ Practice Test & Solutions: Integral Calculus MCQ Level - 2 (10 Questions)

You can prepare effectively for Physics Topic wise Tests for IIT JAM Physics with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Integral Calculus MCQ Level - 2". These 10 questions have been designed by the experts with the latest curriculum of Physics 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 45 minutes
  • - Number of Questions: 10

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Integral Calculus MCQ Level - 2 - Question 1

The area of the figure bounded by the straight lines x = 0, x = 2 and the curves y = 2x and y = 2x – x2 is :

Detailed Solution: Question 1

The required area will be  


The correct answer is:  

Integral Calculus MCQ Level - 2 - Question 2

The area of the region inside the curve r = a cosθ and outside the cardioid r = a(1 – cos θ)  will be :

Detailed Solution: Question 2

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

∴   The required area will be given by,



The correct answer is: 

Integral Calculus MCQ Level - 2 - Question 3

The area bounded by the curves  y2 = x – 1, 2y = xx – axis and y – axis will be equal to :

Detailed Solution: Question 3

The required area will be given by


The correct answer is: 1/3 sq.units

Integral Calculus MCQ Level - 2 - Question 4

The area contained between the curve  and x – axis is :

Detailed Solution: Question 4

The curve is symmetrical about y-axis

Hence, the required area will be,

The correct answer is: πa2 sq. units

Integral Calculus MCQ Level - 2 - Question 5

The area included between the circles r = 2acosθ, r = 2bcosθ; a > b  is equal to :

Detailed Solution: Question 5

The required area will be given by



The correct answer is: 

Integral Calculus MCQ Level - 2 - Question 6

The area of the region R, R : r = a(2 – cos2θ),  0 < θ < 2π will be :

Detailed Solution: Question 6

The required area will be given by


The correct answer is:  

Integral Calculus MCQ Level - 2 - Question 7

The area of the cardioid r = a(1 + cosθ)  lying above x–axis is :

Detailed Solution: Question 7

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




The correct answer is:  

Integral Calculus MCQ Level - 2 - Question 8

The area lying inside the cardioid r = a(1 + cos θ) and outside the circle r = a is :

Detailed Solution: Question 8

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

∴   The required area


The correct answer is: 

Integral Calculus MCQ Level - 2 - Question 9

The area bounded by the curve y = log x and y = (log x)2 is :

Detailed Solution: Question 9

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

Integral Calculus MCQ Level - 2 - Question 10

The area bounded by y = 1 + 2sin2x, x – axis, x = 0 and  x = π  is :

Detailed Solution: Question 10

For x ∈ (0, π) y = 1 + sin2x is a non negative, function.
∴ The area bounded. by y = 1 + 2sin2xx-axis, x = 0 and x = π will be in first quadrant.
∴ The area required  

The correct answer is: 2π sq. units

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