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All questions of Definite Integrals for JEE Exam
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
|
|
Om Desai answered |
In the question, it should be f’(2) instead of f”(2)
Explanation:- f(x) = ∫(0 to x) log(1+x2)
f’(x) = 2xdx/(1+x2)
f’(2) = 2(2)/(1+(2)2)
= 4/5
Explanation:- f(x) = ∫(0 to x) log(1+x2)
f’(x) = 2xdx/(1+x2)
f’(2) = 2(2)/(1+(2)2)
= 4/5
then the value of k is:
- 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:
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)
|
Arjun Singh answered |
Break the integration in two limits from -1 to 0 and 0 to 1 and then integrate
For limit -1 to 0 e^|x| will become e^-x and for 0 to 1 that will be e^+x
For limit -1 to 0 e^|x| will become e^-x and for 0 to 1 that will be e^+x
- 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:
- 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
is:
is:
The value of definite integral depends on- a)The function, the interval and the variable of integration
- b)The function and the variable of integration
- c)The function and the interval
- d)The interval and the variable of integration
Correct answer is option 'C'. Can you explain this answer?
The value of definite integral depends on
a)
The function, the interval and the variable of integration
b)
The function and the variable of integration
c)
The function and the interval
d)
The interval and the variable of integration
|
|
Janani Pillai answered |
Understanding the Definite Integral
The value of a definite integral is influenced by specific factors. The correct answer is option 'C', which states that the value depends on the function and the interval.
Key Factors Affecting Definite Integral
Why Other Options Are Incorrect
Conclusion
In summary, the value of a definite integral is determined by the function being integrated and the interval over which it is evaluated. Understanding these components is essential for solving integral problems effectively in calculus.
The value of a definite integral is influenced by specific factors. The correct answer is option 'C', which states that the value depends on the function and the interval.
Key Factors Affecting Definite Integral
- The Function:
- The definite integral is fundamentally about the area under the curve of a given function over a specified interval.
- Different functions will yield different areas when integrated, hence the value of the integral varies with the function itself. - The Interval:
- The limits of integration, or the interval, play a crucial role.
- Changing the interval will generally change the area under the curve, thus affecting the integral's value.
- For instance, integrating from a to b will provide a different area than integrating from c to d, even if the function remains the same.
Why Other Options Are Incorrect
- Option A: Includes the variable of integration, but this is not a determining factor for the value of the integral. The variable is a placeholder and does not affect the outcome.
- Option B: Omits the interval, which is essential. Without specifying the limits, the integral's value cannot be accurately determined.
- Option D: While it mentions the interval and variable, it neglects the function, which is crucial for calculating the integral.
Conclusion
In summary, the value of a definite integral is determined by the function being integrated and the interval over which it is evaluated. Understanding these components is essential for solving integral problems effectively in calculus.
is equal to 
If f (x) be a function such that 
- a)x log (x e)
- b)
- c)
- d)
Correct answer is option 'C'. Can you explain this answer?
If f (x) be a function such that
a)
x log (x e)
b)
c)
d)
|
Lekshmi Bose answered |
∫ log xdx = xlog x - x = x(log x -1)
= x(log x - log e) =
dx can be evaluated by the substitution
- a)
- b)0
- c)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
a)
b)
0
c)
d)
none of these
|
Ruchi Yadav answered |
Note that sin9x is an odd function, therefore, 
- a)
- b)
- c)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
a)
b)
c)
d)
none of these
|
|
Ruchi Yadav answered |
Dividing numerator and denominator by cos2x and substituting tanx = t , we get :
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