Advertisements
Advertisements
प्रश्न
Evaluate: `int_1^4 {|x -1|+|x - 2|+|x - 4|}dx`
Advertisements
उत्तर १
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
उत्तर २
संबंधित प्रश्न
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_2^8 |x - 5| dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi (x dx)/(1+ sin x)`
Evaluate`int (1)/(x(3+log x))dx`
Find `dy/dx, if y = cos^-1 ( sin 5x)`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 *dx`
`int_0^1 "e"^(2x) "d"x` = ______
Evaluate `int_1^2 (sqrt(x))/(sqrt(3 - x) + sqrt(x)) "d"x`
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_0^1 "dx"/(sqrt(1 + x) - sqrtx)` = ?
`int_(-1)^1 (x + x^3)/(9 - x^2) "d"x` = ______.
`int_0^(2"a") "f"("x") "dx" = int_0^"a" "f"("x") "dx" + int_0^"a" "f"("k" - "x") "dx"`, then the value of k is:
Evaluate:
`int_2^8 (sqrt(10 - "x"))/(sqrt"x" + sqrt(10 - "x")) "dx"`
`int_a^b f(x)dx = int_a^b f(x - a - b)dx`.
`int_4^9 1/sqrt(x)dx` = ______.
If f(x) = `(2 - xcosx)/(2 + xcosx)` and g(x) = logex, (x > 0) then the value of the integral `int_((-π)/4)^(π/4) "g"("f"(x))"d"x` is ______.
Let f be continuous periodic function with period 3, such that `int_0^3f(x)dx` = 1. Then the value of `int_-4^8f(2x)dx` is ______.
Evaluate: `int_0^π x/(1 + sinx)dx`.
Evaluate the following definite integral:
`int_-2^3 1/(x + 5) dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Solve the following.
`int_0^1 e^(x^2) x^3dx`
Evaluate the following definite intergral:
`int_1^2 (3x)/(9x^2 - 1) dx`
Evaluate:
`int_0^sqrt(2)[x^2]dx`
`∫_0^(π/2) (sqrttan x + sqrtcot x)dx` = ______.
Which property is useful for piecewise functions or modulus (absolute value) functions?
Which formula is \[P_5\] : Halving the Upper Limit (Addition)?
If \[f(-x)=-f(x)\], what is \[\int_{-a}^{a} f(x)\,dx\]?
If \[I=\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\frac{dx}{1+\sqrt{\tan x}}\], what is the value of \[I\]?
