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QUESTION: 1

The area of the region bounded by the curves *y* = |*x* – 1| and *y* = 3 – |*x*| is :

Solution:

The required area can be divided into, three regions

= 2 – 1 + 2 + 8 – 4 – 4 +1

= 4 sq. units

The correct answer is: 4 sq. units

QUESTION: 2

The area enclosed between the curve y = log(x + e) and the coordinate axes is :

Solution:

The area will be given by

= ** e** –

= 1 sq. unit

The correct answer is: 1 sq. unit

QUESTION: 3

The area of the plane, region bounded by the curves x + 2y^{2} = 0 and x + 3y^{2} = 1 is equal to :

Solution:

The required area is

The correct answer is 4/3 sq.units

QUESTION: 4

The value of

Solution:

After changing the order, we get

The correct answer is:

QUESTION: 5

The area bounded by the curve y = 2x – x^{2} and the straight line y = –x is given by :

Solution:

The required area is bounded by the curves

∴ The area will be given by

The correct answer is: 9/2 sq.units

QUESTION: 6

The change of order of integration of the integral

Solution:

The region of integration is

Hence, changing the order of integration, we get,

The correct answer is:

QUESTION: 7

The area bounded by the curves |x| + |*y*| ≥ 1 and *x*^{2} + *y*^{2} ≤ 1 is :

Solution:

The required area can be evaluated by

Aliter: Required area = Area of circle – Area of square.

= (π - 2)

sq. units

The correct answer is: (π - 2) sq. units

QUESTION: 8

The area of the region bounded by the curves *y* = |*x* – 2|, *x* = 1, *x* = 3 and the *x–*axis is :

Solution:

The required area is

The correct answer is: 1 sq. unit

QUESTION: 9

The integral becomes after reversing the order of integration.

Then the incorrect option would be :

Solution:

The given region of integration is bounded by

plotting all these curves, we have

Reversing the order of integration, we have the domain of integration divided into 2 regions – I and II.

∴ The integral becomes:

The correct answer is: Q = e

QUESTION: 10

is equivalent to :

Solution:

The region of integration is bounded by and

Changing the order of integration,

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