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All questions of Definite Integrals for JEE Exam
- a)3/2
- b)5/2
- c)3
- d)5
Correct answer is option 'B'. Can you explain this answer?
a)
3/2
b)
5/2
c)
3
d)
5
|
|
Himanshu Dubey answered |
Here u can simple write logx=t... and dont miss limits will change accordingly and mod will also break
The value of 
is- a)0
- b)3/8
- c)4/3
- d)3/4
Correct answer is option 'C'. Can you explain this answer?
The value of is
isa)
0
b)
3/8
c)
4/3
d)
3/4
|
Poonam Reddy answered |
Since sinq is positive in interval (0, π)
Evaluate as limit of sum 
- a)20/5
- b)15/2
- c)20/3
- d)3/20
Correct answer is option 'C'. Can you explain this answer?
Evaluate as limit of sum
a)
20/5
b)
15/2
c)
20/3
d)
3/20
|
Om Desai answered |
∫(0 to 2)(x2 + x + 1)dx
= (0 to 2) [x3/3 + x2/2 + x]½
= [8/3 + 4/2 + 2]
= 40/6
= 20/3
= (0 to 2) [x3/3 + x2/2 + x]½
= [8/3 + 4/2 + 2]
= 40/6
= 20/3
Evaluate: 
- a)1/2
- b)1/4
- c)1
- d)1/8
Correct answer is option 'B'. Can you explain this answer?
Evaluate:
a)
1/2
b)
1/4
c)
1
d)
1/8
|
Sumair Sadiq answered |
This is maths questions I can explain it but you know it is not possible here because this app is not allow to take photo but try it ok let tan inverce 4x =t diff both side wrt x 4x³/1+x⁴ Ka square
x cube / 1+ x8 =dt/4 I = £ 0 se pie by 2 (because when x= 0 t = pie by 2and x = infinity then t = 0 )
I = 1/4 £ 0 se pie by 2 sin t l = 1/4 (- cos t limit 0 se pie by 2 )l = 1/4 ( - cos pie by 2 + cos 0) l = 1/4 ( 0+ 1) l= 1/4 × 1l= 1/4
use my WhatsApp number for further questions but only for study 7060398771
x cube / 1+ x8 =dt/4 I = £ 0 se pie by 2 (because when x= 0 t = pie by 2and x = infinity then t = 0 )
I = 1/4 £ 0 se pie by 2 sin t l = 1/4 (- cos t limit 0 se pie by 2 )l = 1/4 ( - cos pie by 2 + cos 0) l = 1/4 ( 0+ 1) l= 1/4 × 1l= 1/4
use my WhatsApp number for further questions but only for study 7060398771
- a)-1
- b)zero
- c)1
- d)2
Correct answer is option 'B'. Can you explain this answer?
a)
-1
b)
zero
c)
1
d)
2
|
Naina Sharma answered |
∫(0 to 4)(x)1/2 - x2 dx
= [[(x)3/2]/(3/2) - x2](0 to 4)
= [[2x3/2]/3 - x2](0 to 4)
= [[2(0)3/2]/3 - (0)2]] - [[2(4)3/2]/3 - (4)2]]
= 0-0
= 0
= [[(x)3/2]/(3/2) - x2](0 to 4)
= [[2x3/2]/3 - x2](0 to 4)
= [[2(0)3/2]/3 - (0)2]] - [[2(4)3/2]/3 - (4)2]]
= 0-0
= 0
is: 
The value of 
is:- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
The value of is:
is:a)
b)
c)
d)
|
Samyak Jain answered |
1/2(cos π/2 + 1 -[cos(π/2-π/4)+1])=1/2+π/4
If 
is- a)2/3
- b)4/5
- c)1
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
If is
isa)
2/3
b)
4/5
c)
1
d)
None of these
|
Arjun Singh answered |
F'(x)=log(1+x^-2) then differentiate it one time to get f''(x)
then the value of k is:
- a)0
- b) π/8
- c)π2/8
- d)π2/16
Correct answer is option 'D'. Can you explain this answer?
a)
0
b)
π/8
c)
π2/8
d)
π2/16
|
Gaurav Kumar answered |
By adding (i) and (ii), we get
Now, Put tan2x = t, we get
If 
then P =- a)1/3
- b)1/4
- c)1/2
- d)1/5
Correct answer is option 'C'. Can you explain this answer?
If then P =
then P =a)
1/3
b)
1/4
c)
1/2
d)
1/5
|
|
Gaurav Kumar answered |
Comparing it with the given value, we get
- a)
- b)
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
a)
b)
c)
d)
|
Vikas Kapoor answered |
Option d is correct, because it is the property of definite integral
∫02a f(x) dx = ∫0a f(x) dx + ∫0a f(2a – x) dx
∫02a f(x) dx = ∫0a f(x) dx + ∫0a f(2a – x) dx
is:
is:
is equal to
The value of the integral 
is:- a)2e – 1
- b)2e + 1
- c)2e
- d)2(e – 1)
Correct answer is option 'D'. Can you explain this answer?
The value of the integral is:
is:a)
2e – 1
b)
2e + 1
c)
2e
d)
2(e – 1)
|
Aryan Khanna answered |
Correct Answer : d
Explanation : ∫(-1 to 1) e|x| dx
∫(-1 to 0) e|x|dx + ∫(0 to 1) e|x|dx
e1 -1 + e1 - 1
=> 2(e - 1)
- a)20
- b)8
- c)10
- d)18
Correct answer is option 'D'. Can you explain this answer?
a)
20
b)
8
c)
10
d)
18
|
Hardik Handa answered |
Qqqqqqqqqqqqqq
where [.] denote greatest integer function, is equal to- a)-2
- b)-1
- c)-3
- d)-4
Correct answer is option 'C'. Can you explain this answer?
where [.] denote greatest integer function, is equal toa)
-2
b)
-1
c)
-3
d)
-4
|
Rishabh Gupta answered |
First we need to divide this integration in two different parts the first part we have to take the limits from - 1 to 0 and in the next part we have to take the integration from 0 to 1 . then in the first part of -1 to 0 just solve for the greatest internet function for -1 to 0 you will get -3 And do the similar thing for 1 to 0 part and you will 0. add -3 and 0 to get your answer.
- a)if f(2a – x) = – f(x)
- b)if f(2a – x) = f(x)
- c)if f(- x) = f(x)
- d)if f(- x) = – f(x)
Correct answer is option 'D'. Can you explain this answer?
a)
if f(2a – x) = – f(x)
b)
if f(2a – x) = f(x)
c)
if f(- x) = f(x)
d)
if f(- x) = – f(x)
|
|
Om Desai answered |
∫(-a to a)f(x)dx
= ∫(0 to a) [f(x) + f(-x)] if f(x) is an odd function
⇒ f(-x) = -f(x)
= ∫(0 to a) [f(x) + f(-x)] if f(x) is an odd function
⇒ f(-x) = -f(x)
is:
and 
then
is equal to- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
is equal toa)
b)
c)
d)
|
|
Aryan Khanna answered |
Putting xn = t so that n xn–1 dx = dt
If 
then- a)a = 3/2,b=3/2
- b)a = 3/4,b= - 3/4
- c)a = 3/4,b=3/2
- d)a = b
Correct answer is option 'C'. Can you explain this answer?
If then
thena)
a = 3/2,b=3/2
b)
a = 3/4,b= - 3/4
c)
a = 3/4,b=3/2
d)
a = b
|
Sanjeev Kumar answered |
Integrate it by parts taking log (1+ x/2 )as first function
- a)π/2
- b)0
- c) π/4
- d) π/3
Correct answer is option 'B'. Can you explain this answer?
a)
π/2
b)
0
c)
π/4
d)
π/3
|
Infinity Academy answered |
I = ∫0 π2 log(tan x).dx
I = ∫0 π2 log(cot x).dx
Adding both the equations, we get
2I = ∫0 π2 log(tanx) + log(cot x) dx
2I = ∫0 π2 log(1).dx
= 0
I = ∫0 π2 log(cot x).dx
Adding both the equations, we get
2I = ∫0 π2 log(tanx) + log(cot x) dx
2I = ∫0 π2 log(1).dx
= 0
The value of integral 
- a)2
- b)- 1
- c)0
- d)1
Correct answer is option 'D'. Can you explain this answer?
The value of integral
a)
2
b)
- 1
c)
0
d)
1
|
Sushil Kumar answered |
put t = 1/x ⇒ dt = -1/x2 as t = π/2 and π
- a)g (x) h (s) = constant
- b)g (x) = h (x).
- c)g (x) - h (x) = constant
- d)h (x) + g (x) = constant
Correct answer is option 'C'. Can you explain this answer?
a)
g (x) h (s) = constant
b)
g (x) = h (x).
c)
g (x) - h (x) = constant
d)
h (x) + g (x) = constant
|
|
Swati Verma answered |
Since g(x) and h(x) are integrals of the same function , therefore ; g(x) – h(x) is constant.
Find the distance travelled by a car moving with acceleration given by a(t)=Sin(t), if it moves from t = 0 sec to t = π/2 sec, if velocity of a car at t=0sec is 10 km/hr.- a)10.19 km
- b)19.13 km
- c)15.13 km
- d)13.13 km
Correct answer is option 'D'. Can you explain this answer?
Find the distance travelled by a car moving with acceleration given by a(t)=Sin(t), if it moves from t = 0 sec to t = π/2 sec, if velocity of a car at t=0sec is 10 km/hr.
a)
10.19 km
b)
19.13 km
c)
15.13 km
d)
13.13 km
|
Rohit Yadav answered |
Add constant automatically
We know that,
We know that,
- a)log 2
- b)0
- c)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
a)
log 2
b)
0
c)
d)
none of these
|
Shilpa Saha answered |
∫ log(1-x) dx - ∫ log x dx = 0
In 
dy, what is ‘a’ called as?
- a)Integration
- b)Upper limit
- c)Lower limit
- d)Limit of an integral
Correct answer is option 'C'. Can you explain this answer?
In dy, what is ‘a’ called as?
a)
Integration
b)
Upper limit
c)
Lower limit
d)
Limit of an integral
|
|
Anjali Sharma answered |
In 
dy ‘a’ is the called as lower limit and ‘b’ is called the upper limit of the integral. The function f in 
is called the integrand. The letter ‘y’ is a dummy symbol and can be replaced by any other symbol.
- a)0
- b)-2
- c)3
- d)4
Correct answer is option 'A'. Can you explain this answer?
a)
0
b)
-2
c)
3
d)
4
|
Chan singh answered |
Split into two integrals
and 
has the value equal to
Chapter doubts & questions for Definite Integrals - Chapter-wise Tests for JEE Main & Advanced 2025 is part of JEE exam preparation. The chapters have been prepared according to the JEE exam syllabus. The Chapter doubts & questions, notes, tests & MCQs are made for JEE 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests here.
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