Integrals Test

Result

Integrals Test - 5

Score
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Rank
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TIME Taken - -

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Weekly Quiz Competition

Question 1
1 / -0.25

∫sec² x cosec² x dx is equal to

A
tan x + cotx

B
tan x –cot x

C
tan x . cot x

D
none of these.

Solution
Question 2
1 / -0.25

A

B
Log (f(x))

C
f(x)

D
2

Solution
Question 3
1 / -0.25

A
2 √2

B
1

C
2

D
None of these

Solution
Question 4
1 / -0.25

A
log | log (tan x) |

B
tan {log (log x)}

C
log (tan x)

D
tan (log x)

Solution
Question 5
1 / -0.25

A

B
0

C

D
none of these

Solution

Note that sin⁹ x is an odd function, therefore,
Question 6
1 / -0.25

A

B

C

D
none of these

Solution
Question 7
1 / -0.25

A
log 2

B
0

C

D
none of these

Solution

∫ log(1-x) dx - ∫ log x dx = 0
Question 8
1 / -0.25

A
2

B
1

C
√2

D
2 √2

Solution
Question 9
1 / -0.25

A

B

C

D

Solution
Question 10
1 / -0.25

A

B

C

D
none of these

Solution
Question 11
1 / -0.25

∫ (tan x + cot x) dx is equal to

A
log | sin x + cos x|

B
log | cot x|

C
log | tan x|

D
none of these

Solution

Correct Answer :- c

Explanation : ∫(tanx + cotx)dx

= ∫tanxdx + ∫cotxdx

= ∫sinx/cosx dx + ∫cosx/sinx dx

I1 = sinx/cosx

Put t = cosx

dt = -sinx dx

I2 = cosx/sinx

Put t = sinx

dt = cosx dx

So, we get

=>∫-dt/t + ∫dt/t

=>- ln t + ln t + c

=>-ln cosx + ln sinx + c

=>log (sinx/cosx) + c

=>log(tanx)
Question 12
1 / -0.25

∫ log(log x) + (log x)^-1 ) dx is equal to

A
x log (log x)

B
x log (log x)+

C
x log (log x) -

D
none of these.

Solution
Question 13
1 / -0.25

A
−πlog 2

B

C

D
πlog 2

Solution
Question 14
1 / -0.25

A

B

C

D
none of these.

Solution
Question 15
1 / -0.25

A

B

C
0

D
none of these

Solution