Advertisements
Advertisements
Question
Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`
Advertisements
Solution
`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`
APPEARS IN
RELATED QUESTIONS
Evaluate: `int1/(xlogxlog(logx))dx`
Evaluate :
`∫_0^π(4x sin x)/(1+cos^2 x) dx`
Evaluate the integral by using substitution.
`int_0^1 sin^(-1) ((2x)/(1+ x^2)) dx`
Evaluate the integral by using substitution.
`int_0^2 dx/(x + 4 - x^2)`
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate:
Evaluate :
Evaluate the following integral:
Evaluate the following integral:
\[\int\limits_0^2 \left| x^2 - 3x + 2 \right| dx\]
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Find : \[\int e^{2x} \sin \left( 3x + 1 \right) dx\] .
Evaluate: \[\int\limits_0^{\pi/2} \frac{x \sin x \cos x}{\sin^4 x + \cos^4 x}dx\] .
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
If `I_n = int_0^(pi/4) tan^n theta "d"theta " then " I_8 + I_6` equals ______.
`int_0^(pi4) sec^4x "d"x` = ______.
Find: `int (dx)/sqrt(3 - 2x - x^2)`
Evaluate: `int x/(x^2 + 1)"d"x`
