CameraIcon

SearchIcon

MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Integration as Antiderivative

Find the valu...

Question

Find the value of $\int_{- 1}^{1} [x^{2} + {x}] d x$ , where $[\cdot]$ and ${\cdot}$ denote the greatest function and fractional parts of $x$ , respectively.

Open in App

Solution

A] To find period of
$f (x) = s i n 3 x c o s [3 x] - c o s 3 x s i n [3 x]$
As
$s i n (A - B) = s i n A c o s B - c o s A s i n B$
So, $s i n 3 x c o s [3 x] - c o s 3 x s i n [3 x]$
$= s i n (3 x - [3 x])$
As $x - [x] = {x}$
So, $s i n (3 x - [3 x])$
$= s i n ({3 x})$
The period of fractional part of
x is 0 to 1
so, period of
$f (x) = s i n {3 x}$
is $\frac{1}{3}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The value of

\int_{0}^{[x]} {x} d x

(where [.] and {.} denotes greatest integer and fraction part function respectively ) is

Q. The value of

lim x \to 0 ([x] + \sqrt{{x}})

[.]

{}

denote the greatest integer function and fractional part function respectively )

Q. The value of

{s i n^{- 1} [x^{2} + \frac{1}{2}] + c o s^{- 1} [x^{2} - \frac{1}{2}]}

is :
where {.} and [.] denote fractional part function and greatest integer function respectively

[x] {x} = x

[\cdot]

{\cdot}

denote the greatest integer function and fractional part, respectively.
Which of the following is true

Q. Total number of positive real values of x satisfying

2 [x] = x + {x}

[.]

and {.} denote the greatest integer function and fractional part respectively, is equal to

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Integration as Anti-Derivative

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Integration as Antiderivative

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon