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
Evaluate : `int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx`
Evaluate `int_(-2)^2x^2/(1+5^x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) (cos^5 xdx)/(sin^5 x + cos^5 x)`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi (x dx)/(1+ sin x)`
\[\int\limits_0^a 3 x^2 dx = 8,\] find the value of a.
Evaluate`int (1)/(x(3+log x))dx`
Evaluate : `int "x"^2/("x"^4 + 5"x"^2 + 6) "dx"`
Prove that `int_0^"a" "f" ("x") "dx" = int_0^"a" "f" ("a" - "x") "d x",` hence evaluate `int_0^pi ("x" sin "x")/(1 + cos^2 "x") "dx"`
Find : `int_ (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.
Evaluate the following integrals : `int_2^5 sqrt(x)/(sqrt(x) + sqrt(7 - x))*dx`
`int_"a"^"b" "f"(x) "d"x` = ______
Choose the correct alternative:
`int_(-9)^9 x^3/(4 - x^2) "d"x` =
Evaluate `int_1^3 x^2*log x "d"x`
`int_0^1 (1 - x/(1!) + x^2/(2!) - x^3/(3!) + ... "upto" ∞)` e2x dx = ?
`int_0^{pi/2}((3sqrtsecx)/(3sqrtsecx + 3sqrt(cosecx)))dx` = ______
`int_0^1 x tan^-1x dx` = ______
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
`int_0^1 log(1/x - 1) "dx"` = ______.
Which of the following is true?
`int_0^1 "e"^(5logx) "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_(-2)^2 |x cos pix| "d"x` is equal to ______.
`int_0^(pi/2) cos x "e"^(sinx) "d"x` is equal to ______.
If `intxf(x)dx = (f(x))/2` then f(x) = ex.
If `int_0^1(sqrt(2x) - sqrt(2x - x^2))dx = int_0^1(1 - sqrt(1 - y^2) - y^2/2)dy + int_1^2(2 - y^2/2)dy` + I then I equal.
Let a be a positive real number such that `int_0^ae^(x-[x])dx` = 10e – 9 where [x] is the greatest integer less than or equal to x. Then, a is equal to ______.
Solve the following.
`int_0^1 e^(x^2) x^3dx`
Solve the following.
`int_2^3x/((x+2)(x+3))dx`
Evaluate the following integral:
`int_0^1x(1 - x)^5dx`
`∫_0^(π/2) (sqrttan x + sqrtcot x)dx` = ______.
