English
CBSECommerce (English Medium) Class 12
Question Papers3000
Textbook Solutions36125
MCQ Online Mock Tests42
Important Solutions23873
Concept Notes & Videos697
Time Tables25
Syllabus

Evaluate: ∫ 5 1 { | X − 1 | + | X − 2 | + | X − 3 | } D X .

Advertisements
Advertisements

Question

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.

Sum
Advertisements

Solution

= `int_1^5 {| x - 1| + | x - 2| + |x - 3|} dx`

= `int_1^5 (x - 1)dx + int_1^2 (2 - x)dx + int_2^5 (x - 2) dx + int_1^3 (3 - x) dx + int_3^5 ( x - 3) dx`

= `[x^2/2 - x]_1^5 + [2x - x^2/2]_1^2 + [x^2/2 - 2x]_2^5 + [3x - x^2/2]_1^3 + [x^2/3 - 3x]_3^5`

= 17

shaalaa.com
Evaluation of Definite Integrals
  Is there an error in this question or solution?
Q 12.1
2015-2016 (March) All India Set 1 E

APPEARS IN

2015-2016 (March) All India Set 1 E (with solutions)
Q 12.1 | 4 marks

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Evaluate:  `int (1+logx)/(x(2+logx)(3+logx))dx`


Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`


 

Evaluate `int_(-1)^2|x^3-x|dx`

 

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`


Evaluate the integral by using substitution.

`int_0^1 x/(x^2 +1)`dx


Evaluate the integral by using substitution.

`int_0^2 xsqrt(x+2)`  (Put x + 2 = `t^2`)


Evaluate the integral by using substitution.

`int_1^2 (1/x- 1/(2x^2))e^(2x) dx`


Evaluate of the following integral: 

\[\int x^\frac{5}{4} dx\]

Evaluate the following integral:

\[\int\limits_{- 4}^4 \left| x + 2 \right| dx\]

Evaluate the following integral:

\[\int\limits_{- 2}^2 \left| x + 1 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_0^{\pi/2} \left| \cos 2x \right| dx\]

Evaluate the following integral:

\[\int\limits_{- \pi/4}^{\pi/4} \left| \sin x \right| dx\]

Evaluate the following integral:

\[\int\limits_2^8 \left| x - 5 \right| dx\]

 


Evaluate the following integral:

\[\int\limits_1^4 \left\{ \left| x - 1 \right| + \left| x - 2 \right| + \left| x - 4 \right| \right\} dx\]

 


Evaluate each of the following integral:

\[\int_\frac{\pi}{6}^\frac{\pi}{3} \frac{\sqrt{\tan x}}{\sqrt{\tan x} + \sqrt{\cot x}}dx\]

Evaluate each of the following integral:

\[\int_{- \frac{\pi}{2}}^\frac{\pi}{2} \frac{\cos^2 x}{1 + e^x}dx\]

\[\int\limits_0^a \frac{\sqrt{x}}{\sqrt{x} + \sqrt{a - x}} dx\]

Evaluate the following integral:

\[\int_2^8 \frac{\sqrt{10 - x}}{\sqrt{x} + \sqrt{10 - x}}dx\]

Evaluate the following integral:

\[\int_0^\pi x\sin x \cos^2 xdx\]

Evaluate the following integral:

\[\int_{- 2}^2 \frac{3 x^3 + 2\left| x \right| + 1}{x^2 + \left| x \right| + 1}dx\]

Evaluate : \[\int\limits_{- 2}^1 \left| x^3 - x \right|dx\] .


Find: `int_  (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.


Evaluate the following:

`int ("e"^(6logx) - "e"^(5logx))/("e"^(4logx) - "e"^(3logx)) "d"x`


Each student in a class of 40, studies at least one of the subjects English, Mathematics and Economics. 16 study English, 22 Economics and 26 Mathematics, 5 study English and Economics, 14 Mathematics and Economics and 2 study all the three subjects. The number of students who study English and Mathematics but not Economics is


Which limits are used to evaluate the resulting expression in Method: Resubstitution?


If the substitution is \[t=g(x)\], what differential relation is used in Method 2: Changing the Limits?


If \[t=\tan^{-1}x\], what is \[dt\]?


After using \[t=\tan^{-1}x\] in \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\], which integral results?


What is the value of \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\]?


Share
Notifications

Englishहिंदीमराठी
Login
Create free account


      Forgot password?
Course
Use app×