Description

This mock test of Test: Area Between A Curve And A Line for JEE helps you for every JEE entrance exam.
This contains 10 Multiple Choice Questions for JEE Test: Area Between A Curve And A Line (mcq) to study with solutions a complete question bank.
The solved questions answers in this Test: Area Between A Curve And A Line quiz give you a good mix of easy questions and tough questions. JEE
students definitely take this Test: Area Between A Curve And A Line exercise for a better result in the exam. You can find other Test: Area Between A Curve And A Line extra questions,
long questions & short questions for JEE on EduRev as well by searching above.

QUESTION: 1

The area enclosed between the lines x = 2 and x = 7 is

Solution:

Area enclosed between the lines x = 2 and x = 7 is Infinite.

QUESTION: 2

If the area of y = f(x) between x = a and x = b is then the point c is the point of intersection of the curve with:

Solution:

QUESTION: 3

Area under the circle x^{2} + y^{2} = 16 is

Solution:

QUESTION: 4

Area of the shaded region in the given figure is :

Solution:

QUESTION: 5

Area of the region bounded by the curve y^{2} = 2y – x and y-axis is:

Solution:

y^{2 }= 2y−x

⇒ x = 2y − y^{2}

Curve meets y−axis where x= 0

2y − y^{2 }= 0

⇒ y (2−y) = 0

y = 0 or y = 2

Area =∣∫(0 to 2) x.dy∣

=|∫(0 to 2) (2y − y^{2}).dy∣

=∣[y^{2} − y^{3}/3] (0 to 2) |[4−8/3]−0|

=4/3 unit^{2}

QUESTION: 6

The area of the region bounded between the line x=9 and the parabola y^{2}=16x is

Solution:

**Correct Answer : a**

**Explanation : **Equation of the parabola is

y2 = 16x .... (i)

Required area =2∫(0 to 9) ydx

[by symmetry about x-axis]

= 2∫(0 to 9) 4(x)^{1/2} dx

= 8∫(0 to 9) (x)^{1/2} dx

= 8[(x^{3/2})/(3/2)](0 to 9)

= 16/3[x^{3/2}](0 to 9)

= 144 sq unit.

QUESTION: 7

Area of the region is :

Solution:

QUESTION: 8

If the area above x-axis, bounded by the curves y = 2^{kx}, x = 0 and x = 2 is then k = ?

Solution:

QUESTION: 9

Write the shaded region as an integral

Solution:

QUESTION: 10

The area bounded by the curve:

y = cos^{2} x between x = 0, x = π and x axis

Solution:

y = cos^{2} x [0,π]

∫(0 to π/2)cos^{2} xdx + ∫(π/2 to π)cos^{2} xdx

= 1/2∫(1 + cos 2x)

= [½(x + sin(2x)/2](0 to π/2] + [1/2(x + sin(2x)/2](π/2 to π)

= ½|π + 0 - 0 - 0| + 1/2|(π + 0) - π/2|

= π/4 + π/4 = π/2

### Example Area bounded by curve, line - Application of Integrals

Video | 13:22 min

### Area under VT curve - Motion in a Straight Line

Video | 05:42 min

### Examples : Area bounded by a curve and a line

Video | 14:33 min

### Area between curves

Video | 04:09 min

- Test: Area Between A Curve And A Line
Test | 10 questions | 10 min

- Test: Area Between Two Curves
Test | 10 questions | 10 min

- Test: Area Under Curve With Solution (Competition Level)
Test | 30 questions | 60 min

- Test: Flash Vaporization Line (Q-line)
Test | 10 questions | 20 min

- Test: Line Integral
Test | 10 questions | 10 min