हिंदी

Evaluate : ∫40(|x|+|x−2|+|x−4|)dx - Mathematics

Advertisements
Advertisements

प्रश्न

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

Advertisements

उत्तर

 `int_0^4(|x|+|x-2|+|x-4|)dx`

`I=int_0^4f(x)dx=int_0^2f(x)dx+int_2^4f(x)dx`

`I=int_0^2(x+2-x+4-x)dx+int_2^4(x+x-2+4-x)dx`

`I=int_0^2(x+2-x+4-x)dx+int_2^4(x+x-2+4-x)dx`

`I=int_0^2(6-x)dx+int_2^4(x+2)dx=[6x-x^2/2]_0^2+[x^2/2+2x]_2^4=[12-1]+[8-2+(8-4)]=20`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2012-2013 (March) Delhi Set 1

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Evaluate : `int1/(3+5cosx)dx`


 

Evaluate `int_(-1)^2|x^3-x|dx`

 

Evaluate the integral by using substitution.

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


Evaluate the integral by using substitution.

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


The value of the integral `int_(1/3)^4 ((x- x^3)^(1/3))/x^4` dx is ______.


If `f(x) = int_0^pi t sin  t  dt`, then f' (x) is ______.


Evaluate of the following integral: 

\[\int\frac{1}{x^5}dx\]

Evaluate of the following integral:

\[\int\frac{1}{\sqrt[3]{x^2}}dx\]

Evaluate the following definite integral:

\[\int_0^1 \frac{1}{\sqrt{\left( x - 1 \right)\left( 2 - x \right)}}dx\]

Evaluate the following integral:

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

Evaluate the following integral:

\[\int\limits_0^3 \left| 3x - 1 \right| dx\]

 


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:

\[\int\limits_0^4 \left( \left| x \right| + \left| x - 2 \right| + \left| x - 4 \right| \right) dx\]

Evaluate the following integral:

\[\int_0^\frac{\pi}{2} \frac{\tan^7 x}{\tan^7 x + \cot^7 x}dx\]

Evaluate the following integral:

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

Evaluate the following integral:

\[\int_{- \pi}^\pi \frac{2x\left( 1 + \sin x \right)}{1 + \cos^2 x}dx\]

Evaluate the following integral:

\[\int_0^\pi \left( \frac{x}{1 + \sin^2 x} + \cos^7 x \right)dx\]

Evaluate the following integral:

\[\int_0^{2\pi} \sin^{100} x \cos^{101} xdx\]

 


Find : \[\int\frac{x \sin^{- 1} x}{\sqrt{1 - x^2}}dx\] .


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


Find: `int (dx)/sqrt(3 - 2x - x^2)`


Evaluate:

`int (1 + cosx)/(sin^2x)dx`


If `int x^5 cos (x^6)dx = k sin (x^6) + C`, find the value of k.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×