Bihar Board Solutions: Bihar Board 12th Maths Objective Answers Chapter 7 Integrals
Bihar Board Solutions: Bihar Board 12th Maths Objective Answers Chapter 7 Integrals
Bihar Board Solutions: Bihar Board 12th Maths Objective Answers Chapter 7 Integrals
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Question 2.
Answer:
x a+1
﴾a﴿
a x a
+ + a x + C
log a a+1
Question 3.
Answer:
﴾a﴿ − 14 tan(7 − 4x) + C
Question 4.
Answer:
x
2
﴾a﴿ 1
3
2
2
+ C
(log 2)
Question 5.
Answer:
4
﴾b﴿ − cos4
4
x
+ C
Question 6.
Answer:
﴾a﴿
−3
3
+ C
√sin x
Question 7.
Evaluate: ∫tan﴾x – θ﴿ tan﴾x + θ﴿ tan2x dx
﴾a﴿ 12 log|cos2x| – log|cos﴾x – θ﴿| + log|cos﴾x + θ﴿| + C
﴾b﴿ – 12 log|cos2x| + log|cos﴾x – θ﴿| + log|cos ﴾x + θ﴿| + C
﴾c﴿ – 12 log|cos2x| – log|cos﴾x – θ﴿| – log|cos﴾x + θ﴿| + C
﴾d﴿ None of these
Answer:
﴾b﴿ – 12 log|cos2x| + log|cos﴾x – θ﴿| + log|cos ﴾x + θ﴿| + C
Question 8.
Answer:
﴾b﴿ − 2 +
2
3
3/2
(tan x) + C
√tan x
Question 9.
Answer:
﴾b﴿ − 35 tan−5/3 x + 3 tan1/3 x + C
Question 10.
Answer:
2
﴾c﴿
x −3
1 4 1 ∣ ∣
log∣
∣x − 9∣
∣ − + C
4 12 ∣ 2
x +3 ∣
Question 11.
Answer:
−− −− −−−
﴾b﴿ − log∣∣e−x + √e
−2x
− 1∣
∣ + C
Question 12.
Answer:
n
﴾b﴿ n1 log∣∣ x +1 ∣∣ + C
x
n
Question 13.
Answer:
﴾c﴿ 16 tan−1 ( 2 tan
3
x
) + C
Question 14.
Answer:
− − − −
﴾c﴿ 2√x − 3(√x) + 6(√x) − 6 log(√x + 1) + C
3 6 6
Question 15.
Answer:
1 1 2
− log |1 + tan θ| + log∣
∣tan θ − tan θ + 1∣
∣
3 6
Question 16.
Answer:
﴾a﴿ log | sec x + tan x| − 2 tan(x/2) + C
Question 17.
Answer:
﴾c﴿ tan x2
Question 18.
Answer:
x
﴾a﴿ 1+sin x
e cos x
+ C
Question 19.
Answer:
﴾b﴿ ex ( x+4 ) + C
x+2
Question 20.
Answer:
1 −−−−−−−−−
2
(x + 1)√x + 2x + 5
﴾b﴿ 2
−−−−−−−−−
2
+2 log |(x + 1) + √x + 2x + 5 | + C
Question 21.
2 2
∫ x dx
1
﴾a﴿ 1
﴾b﴿ 73
﴾c﴿ 1
﴾d﴿ 0
Answer:
﴾b﴿ 73
Question 22.
2 2
∫ (x + 3) dx
0
﴾a﴿
25
﴾b﴿
26
﴾c﴿ 24
Question 23.
−−−− −− −−
Evaluate: ∫0
π/4
√1 − sin 2x dx
﴾a﴿ √2 – 1
﴾b﴿ √2 + 1
﴾c﴿ √2
﴾d﴿ None of these
Answer:
﴾a﴿ √2 – 1
Question 24.
Evaluate: ∫0
2π π x
sin( + )dx
4 2
﴾a﴿ ‐2√2
﴾b﴿ ‐2
﴾c﴿ √2
﴾d﴿ 2√2
Answer:
﴾d﴿ 2√2
Question 25.
Evaluate: ∫1
2 dx
2
x
﴾a﴿ 1
﴾b﴿ 1
﴾c﴿ 2
﴾d﴿ ‐1
Answer:
﴾a﴿ 12
Question 26.
Evaluate: ∫0
1 −1 2x
sin ( 2
)dx
1+x
﴾a﴿ – log2
π
﴾b﴿ π
﴾c﴿ 4
π
﴾d﴿ – log2
π
Answer:
﴾a﴿ 2 – log2
π
Question 27.
Answer:
﴾a﴿ log( 43 )
Question 28.
Answer:
﴾c﴿
4−π
4√2
Question 29.
Answer:
﴾c﴿ 2
tan
−1
(
1
)
√5 √5
Question 30.
Answer:
﴾c﴿ 1 3+√5
log( )
√5 2
Question 31.
Answer:
﴾a﴿ π2
Question 32.
Answer:
﴾a﴿ 21
8
Question 33.
Answer:
﴾a﴿ 2 – √2
Question 34.
Answer:
﴾b﴿ 12 + 1
π+2
− A
Question 35.
Answer:
﴾d﴿ π2
Question 36.
Answer:
﴾c﴿ π2
Question 37.
Answer:
﴾c﴿ cosec(b − a) log∣∣
sin(x−b)
∣
+ C
sin(x−a) ∣
Question 38.
Answer:
x
﴾a﴿ 1+x
e
2
+ C
Question 39.
Answer:
﴾d﴿ x −
2 3
x x
+ − log |1 + x| + C
2 3
Question 40.
Answer:
﴾d﴿ a = 13 , b = ‐1
Question 41.
Answer:
﴾a﴿ 1
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