Test: Area Between A Curve And A Line


10 Questions MCQ Test Mathematics (Maths) Class 12 | Test: Area Between A Curve And A Line


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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 x2 + y2 = 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 y2 = 2y – x and y-axis is:​

Solution:

y= 2y−x
⇒ x = 2y − y2
Curve meets y−axis where x= 0
2y − y= 0
⇒ y (2−y) = 0
y = 0 or y = 2
Area =∣∫(0 to 2) x.dy∣
=|∫(0 to 2) (2y − y2).dy∣
=∣[y2 − y3/3] (0 to 2) |[4−8/3]−0|
=4/3 unit2

QUESTION: 6

The area of the region bounded between the line x=9 and the parabola y2=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[(x3/2)/(3/2)](0 to 9)

​= 16/3[x3/2](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 = 2kx, 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 = cos2 x between x = 0, x = π and x axis

Solution:

y = cos2 x [0,π]
∫(0 to π/2)cos2 xdx + ∫(π/2 to π)cos2 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

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