Integrals Online Objective Test | Integrals Online Objective Test

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q1.

$\int \frac{\log x^{n}}{x} d x, n \in N,$ is equal to

A. (logx)22n+C

n(logx)22+c

C. (logx)2n+C

D. n(logx)2+C

Answer : Option B
Explaination / Solution:

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q2.

\int (\tan x + c o t x)

dx is equal to

A. none of these.

B. log | sin x + cos x|+C

C. log | cot x|+C

D. log | tan x|+C

Answer : Option D
Explaination / Solution:

[−log| cosx|+log| sin x|]=log | tan x|+C

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q3.

\int \frac{\sin 2 x}{3 + 4 \sin^{2} x} d x

is equal to

A. 29tan−1(3tanx2)+C

B. 14log(3+4sin2x)+C

C. 13log(5+7sec2x)+C

D. 23log(tanx2)+C

Answer : Option B
Explaination / Solution:

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q4.

\int \frac{\cos x}{\cos (x - a)}

dx is equal to

A. x cos a + sin a log |cos (x–a)| + C

B. sin a – sin a log | cos ( x – a) |

C. cos a – sin a log | sin ( x – a) | + C

D. x cos a – sin a log | cos ( x – a) |

Answer : Option A
Explaination / Solution:

∫cos((x−a)+a)cos(x−a)dx=∫cos(x−a)cosa−sin(x−a)sinacos(x−a)dx=∫{cosa−sinatan(x−a)}dx.xcosa+sinalog|cos(x–a)|+C

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q5. Which of the following is different from

\int \frac{1}{1 + x^{2}} d x ?

A. −cot−1x+C

B. tan−1x+C

C. None of these

D. π2−cot−1x+C

Answer : Option C
Explaination / Solution:

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q6.

is equal to

A. 12(xsinx+cosx)1/2+C

B. 23(xsinx+cosx)3/2+C

C. 35(xcosx−sinx)3/2+C

D. 2(xsinx+cosx)1/2+C

Answer : Option D
Explaination / Solution:

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q7.

\int \sqrt{a^{2} - x^{2}}

dx is equal to

A. a2a2−x2−−−−−−√+x22log∣∣x+a2−x2−−−−−−√∣∣+C

B. x2a2−x2−−−−−−√+a22log∣∣x+a2−x2−−−−−−√∣∣+C

C. x2a2−x2−−−−−−√−a22sin−1(xa)+C

x2a2−x2−−−−−−√+a22sin−1(xa)+C

Answer : Option D
Explaination / Solution:

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q8.

$\int x^{- 1}$ dx is equal to

A. xee+C

B. loge|x|+C

C. log10x+C

D. logex2+C

Answer : Option B
Explaination / Solution:

∫1xdx=loge|x|+C

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q9. If ∫ f(x) dx = f (x), then

A. f (x) = x

B. f(x) = ex

C. f(x) = ax

D. f (x) = 0

Answer : Option B
Explaination / Solution:

$\frac{d}{d x} (f (x)) = f (x)$

It implies that the function remains same after integrating or differentiating it. So the function must be ex

# Integrals # CBSE 12th Mathematics Prepare / Learn

Q10.

\int \tan^{2}

x dx is equal to

A. tan x +2x + C

2 t a n x \sec^{2} x + C

C. tan3x3+C

D. tan x – x + C

Answer : Option D
Explaination / Solution:

Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0

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