IIT JAM > Topic-wise Tests & Solved Examples for IIT JAM Mathematics > Integral Calculus -2
Integral Calculus -2
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20 Questions MCQ Test Topic-wise Tests & Solved Examples for IIT JAM Mathematics | Integral Calculus -2
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Detailed Solution for Integral Calculus -2 - Question 1
...(i)
....(ii)
Adding (i) and (ii), we get
2l=0
implies 1 = 0
Detailed Solution for Integral Calculus -2 - Question 2
Detailed Solution for Integral Calculus -2 - Question 3
Here f(t) = t3 is continuous function, so from by fundamental theorem of calculus (If f is constinuous on an interval, then f has an anti-derivative on that interval)
Detailed Solution for Integral Calculus -2 - Question 4
mπ, then the value of m is:
Detailed Solution for Integral Calculus -2 - Question 5
Given that
Hence 
| sin x | dx is equal to:
Detailed Solution for Integral Calculus -2 - Question 6
[Since sin x is periodic with period π]
Detailed Solution for Integral Calculus -2 - Question 7
x dx is equal to:
Detailed Solution for Integral Calculus -2 - Question 8
Detailed Solution for Integral Calculus -2 - Question 9
Detailed Solution for Integral Calculus -2 - Question 10
xF(sin X) dx is equal to
Detailed Solution for Integral Calculus -2 - Question 11
...(i)
...(ii)
Adding (i) and (ii), we get
Hence 
= where [ ] represents greatest integer:
Detailed Solution for Integral Calculus -2 - Question 12
Detailed Solution for Integral Calculus -2 - Question 13
Detailed Solution for Integral Calculus -2 - Question 14
dt, then the derivative of f(x) with respect to x is:
Detailed Solution for Integral Calculus -2 - Question 15
Detailed Solution for Integral Calculus -2 - Question 16
Given that
Hence 
Detailed Solution for Integral Calculus -2 - Question 17
is equal to
Detailed Solution for Integral Calculus -2 - Question 18
, x ≠ 0, then 
Detailed Solution for Integral Calculus -2 - Question 19
We have 
x dx is equal to:
Detailed Solution for Integral Calculus -2 - Question 20
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