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
If `int_0^alpha3x^2dx=8` then the value of α is :
(a) 0
(b) -2
(c) 2
(d) ±2
By using the properties of the definite integral, evaluate the integral:
`int_0^1 x(1-x)^n dx`
Evaluate `int e^x [(cosx - sin x)/sin^2 x]dx`
If \[f\left( a + b - x \right) = f\left( x \right)\] , then prove that
Find `dy/dx, if y = cos^-1 ( sin 5x)`
Evaluate : ∫ log (1 + x2) dx
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x)) dx` = ______.
`int_2^4 x/(x^2 + 1) "d"x` = ______
`int_0^4 1/(1 + sqrtx)`dx = ______.
`int_(pi/18)^((4pi)/9) (2 sqrt(sin x))/(sqrt (sin x) + sqrt(cos x))` 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_(pi/4)^(pi/2) sqrt(1-sin 2x) dx =` ______.
`int_-1^1x^2/(1+x^2) dx=` ______.
`int_0^(pi/2) 1/(1 + cosx) "d"x` = ______.
Find `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x)) "d"x`
If `int_0^1 "e"^"t"/(1 + "t") "dt"` = a, then `int_0^1 "e"^"t"/(1 + "t")^2 "dt"` is equal to ______.
`int_0^(2"a") "f"(x) "d"x = 2int_0^"a" "f"(x) "d"x`, if f(2a – x) = ______.
`int (dx)/(e^x + e^(-x))` is equal to ______.
Let f be a real valued continuous function on [0, 1] and f(x) = `x + int_0^1 (x - t)f(t)dt`. Then, which of the following points (x, y) lies on the curve y = f(x)?
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 ______.
`int_0^π(xsinx)/(1 + cos^2x)dx` equals ______.
`int_0^(pi/4) (sec^2x)/((1 + tanx)(2 + tanx))dx` equals ______.
Evaluate: `int_0^π 1/(5 + 4 cos x)dx`
What is `int_0^(π/2)` sin 2x ℓ n (cot x) dx equal to ?
Assertion (A): `int_2^8 sqrt(10 - x)/(sqrt(x) + sqrt(10 - x))dx` = 3.
Reason (R): `int_a^b f(x) dx = int_a^b f(a + b - x) dx`.
For any integer n, the value of `int_-π^π e^(cos^2x) sin^3 (2n + 1)x dx` is ______.
Evaluate : `int_-1^1 log ((2 - x)/(2 + x))dx`.
Evaluate the following integral:
`int_-9^9 x^3 / (4 - x^2) dx`
Solve.
`int_0^1e^(x^2)x^3dx`
