Question # 1

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Integration by parts

Definite integral

Differentiation

None of these

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e^ax

f(x)

e^axf(x)

e^{ax + f(x)}

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equal to each other

not equal to each other

nearly equal to each other

None of these

If the upper limit is a constant and the lower limit is a variable, then the integral is a function of:

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x

y

lower limit

upper limit

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a cosec (ax + b)

cot (ax + b)

If the graph of f is entirely above the x-axis, then the definite integral is _______:

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Positive

Positive or negative

Negative

Positive and negative

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ln |sec x + tan x | + c

ln |cosec x - cot x | + c

ln |sec x - tan x| + c

ln |cosec x + cot x | + c

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cot x

- cot x

cosec x cot x

-cosec x cot x

The technique or method to find such a function whose derivative is given involves the inverse process of differentiation called:

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Differentiation

Integration

Differential

None of these

If the lower limit is a constant and the upper limit is a variable, then the integral is a function of:

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x

y

lower limit

upper limit

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ln |sin x|

- ln |sin x|

ln |cos x|

-ln |cos x|

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domain

range

lower limit

upper limit

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cos x + c

- cos x + c

sin x + c

-sin x + c

If y = sin x then dy =

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cosy dx

cos x

cosx dx

cos xdy

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Integration

Integration w.r.t.x.

Differentiation

Differentiation w.r.t.x

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ln |sec x + tan x | + c

ln |cosec x - cot x | + c

ln |sec x - tan x | + c

ln |cosec x + cot x | + c

The general solution of differential equation of order n contains n arbitrary constants, which can be determined by ------------ initial value conditions.

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1

0

2

n

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2

1

Area between x-axis and the curve:

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32

16

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36

42

48

12

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FSC Part 2 Mathematics Chapter 3 Online Test MCQs With Answers

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