Advertisements
Advertisements
Question
Evaluate: `int_1^4 {|x -1|+|x - 2|+|x - 4|}dx`
Advertisements
Solution 1
I = `int_1^4 (|x -1|+|x - 2|+|x - 4|)dx`
Let f (x) = |x - 1| + |x - 2| + |x - 4|
We have three critical points x = 1, 2, 4
(i) when x <1
(ii) when 1≤ x < 2
(iii) when 2 ≤ x < 4
(iv) when x ≥ 4
Solution 2
RELATED QUESTIONS
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`
Evaluate : `intlogx/(1+logx)^2dx`
Evaluate `int_(-2)^2x^2/(1+5^x)dx`
If `int_0^alpha(3x^2+2x+1)dx=14` then `alpha=`
(A) 1
(B) 2
(C) –1
(D) –2
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/4) log (1+ tan x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi log(1+ cos x) dx`
Using properties of definite integrals, evaluate
`int_0^(π/2) sqrt(sin x )/ (sqrtsin x + sqrtcos x)dx`
`int_1^2 1/(2x + 3) dx` = ______
`int_0^(pi/2) sqrt(cos theta) * sin^2 theta "d" theta` = ______.
`int_0^{pi/2} cos^2x dx` = ______
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
`int_-2^1 dx/(x^2 + 4x + 13)` = ______
`int_{pi/6}^{pi/3} sin^2x dx` = ______
If `int_0^"k" "dx"/(2 + 32x^2) = pi/32,` then the value of k is ______.
`int_(-1)^1 log ((2 - x)/(2 + x)) "dx" = ?`
`int_0^1 log(1/x - 1) "dx"` = ______.
`int_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
Which of the following is true?
`int_a^b f(x)dx = int_a^b f(x - a - b)dx`.
The value of `int_((-1)/sqrt(2))^(1/sqrt(2)) (((x + 1)/(x - 1))^2 + ((x - 1)/(x + 1))^2 - 2)^(1/2)`dx is ______.
The integral `int_0^2||x - 1| -x|dx` is equal to ______.
Let `int_0^∞ (t^4dt)/(1 + t^2)^6 = (3π)/(64k)` then k is equal to ______.
If `int_0^K dx/(2 + 18x^2) = π/24`, then the value of K is ______.
Evaluate `int_-1^1 |x^4 - x|dx`.
Evaluate the following definite integral:
`int_4^9 1/sqrt"x" "dx"`
Solve the following.
`int_1^3 x^2 logx dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Evaluate the following integral:
`int_-9^9 x^3/(4 - x^2) dx`
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Evaluate the following integral:
`int_-9^9x^3/(4-x^2)dx`
