MTH101 short notes or past paper
ye question answer han. mne prepare kiye ha. umeed ha ap ko kuch na kuch samj aa jaye gi Attachments:Download MTH101 Short notes or Past paper
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Assalam o Alaikum MTH101 short notes is attached is above link
plz jis kisi ke pas mth101 ke past final solved paper hn share karain or short notes mil jayain.
plz Comments karain ta ke ziada se zaida student is se kamyab ho sakain
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Hania gud keep it up & thanks for sharing
ردحذفAoa..
حذفMath101 ke important question hain Apke pass?
حذفvery helpful
ردحذفmth101 k short notes chahiye plZzzz koi snd kr dy
ردحذفComplete and Important Question and answer
حذف1. What is the difference between definite integral and an indefinite integral?
If the function f is continuous on [a, b], and can assume both
positive and negative values, the definite integral
( )
b
a
f x dx
is net signed area between y = f(x) and the interval [a, b]. The
numbers a and b are called the lower and upper limits of
integration.
Indefinite integral is the set of functions F(x) + C, where C is constant of integration and F(x) is the
integral of given function f where
( )
( )
d F x
f x
dx
.
Q 2. What is meant by net signed area (the term used in defining definite integral)?
An indefinite integral is of the form
f x dx F x C ( ) ( )
Suppose that a function f has a smooth curve in an interval [a, b] and can lie both above and below xaxis then ‘area under the curve and above x-axis’ minus ‘area above the curve below x-axis’ is termed as
net signed area under the curve of f on the interval [a, b]. It is named "signed" area
because the area above the x -axis counts as positive and the area below the x -axis
counts as negative.Net signed area can be positive, negative or zero; it is positive
when there is more area above than below, negative when there is more area
below than above, and zero when the area above and below are equal.For example,
in the figure
Net signed area under the curve of f on the interval [a, b]
Visit for more... www.vustudy.com
= [Area above] – [Area below]
= (A + C) – B
Q 3. Why we add C with the anti-derivative for evaluating an indefinite integral?
ANSWER: If a function f(x) is defined on an interval and F(x) is an antiderivative of f(x),
then the indefinite integral is set of all anti-derivatives of f(x), that is, the functions F(x) + C,
where C is an arbitrary constant.
As we know, the derivative of any constant function is zero. Once one has found one
antiderivative F(x), adding or subtracting a constant C will give us another antiderivative,
because (F(x) + C) ' = F ' (x) + C ' = F ' (x) . The constant is a way of expressing that
every function has an infinite number of different anti-derivatives.
For example, suppose one wants to find anti-derivatives of cos(x). One such anti-derivative is
sin(x). Another one is sin(x) + 1. A third is sin(x) − π. Each of these has derivative
cos(x), so they are all anti-derivatives of cos(x).
It turns out that adding and subtracting constants is the only flexibility we have in finding
different anti-derivatives of the same function. That is, all anti-derivatives are the same up to a
constant. To express this fact for cos(x), we write:
∫ cos (x) dx = sin(x) + C
mid term ky notes chahiye ye to lecture 32 sy start ho rhy
ردحذفMth 101 vu MCQs are required for preparation mid /grand quiz spring 2020.plz mail me
ردحذفLecture No 23 to 45
حذفComplete and Important Question and answer
1. What is the difference between definite integral and an indefinite integral?
If the function f is continuous on [a, b], and can assume both
positive and negative values, the definite integral
( )
b
a
f x dx
is net signed area between y = f(x) and the interval [a, b]. The
numbers a and b are called the lower and upper limits of
integration.
Indefinite integral is the set of functions F(x) + C, where C is constant of integration and F(x) is the
integral of given function f where
( )
( )
d F x
f x
dx
.
Q 2. What is meant by net signed area (the term used in defining definite integral)?
An indefinite integral is of the form
f x dx F x C ( ) ( )
Suppose that a function f has a smooth curve in an interval [a, b] and can lie both above and below xaxis then ‘area under the curve and above x-axis’ minus ‘area above the curve below x-axis’ is termed as
net signed area under the curve of f on the interval [a, b]. It is named "signed" area
because the area above the x -axis counts as positive and the area below the x -axis
counts as negative.Net signed area can be positive, negative or zero; it is positive
when there is more area above than below, negative when there is more area
below than above, and zero when the area above and below are equal.For example,
in the figure
Net signed area under the curve of f on the interval [a, b]
Visit for more... www.vustudy.com
= [Area above] – [Area below]
= (A + C) – B
Q 3. Why we add C with the anti-derivative for evaluating an indefinite integral?
ANSWER: If a function f(x) is defined on an interval and F(x) is an antiderivative of f(x),
then the indefinite integral is set of all anti-derivatives of f(x), that is, the functions F(x) + C,
where C is an arbitrary constant.
As we know, the derivative of any constant function is zero. Once one has found one
antiderivative F(x), adding or subtracting a constant C will give us another antiderivative,
because (F(x) + C) ' = F ' (x) + C ' = F ' (x) . The constant is a way of expressing that
every function has an infinite number of different anti-derivatives.
For example, suppose one wants to find anti-derivatives of cos(x). One such anti-derivative is
sin(x). Another one is sin(x) + 1. A third is sin(x) − π. Each of these has derivative
cos(x), so they are all anti-derivatives of cos(x).
It turns out that adding and subtracting constants is the only flexibility we have in finding
different anti-derivatives of the same function. That is, all anti-derivatives are the same up to a
constant. To express this fact for cos(x), we write:
∫ cos (x) dx = sin(x) + C
Q 6. State First Fundamental Theorem of Calculus?
The First Fundamental Theorem of Calculus states that:
If f is continuous on the closed interval [a, b] and F is the anti-derivative of f on
[ , ] a b
, then
( ) ( ) ( )
b
a
f x dx F b F a
Q.1# Why we use the second fundamental theorem of calculus?
Answer: The first fundamental theorem of calculus is used to evaluate the definite integral of a
continuous function if we can find an antiderivative for that function, but it does not point out
the question of which functions actually have antiderivatives; then at this stage the second
fundamental theorem of calculus is used.
The second fundamental theorem of calculus states that the derivative of a definite integral
with respect to its upper endpoint is its integrand; it allows one to compute the definite integral
of a function by using any one of its infinitely many antiderivatives. This part of the theorem has
invaluable practical applications, because it markedly simplifies the computation of definite
integral.