Advertisements
Advertisements
Question
Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.
Advertisements
Solution
= `int_1^5 {| x - 1| + | x - 2| + |x - 3|} dx`
= `int_1^5 (x - 1)dx + int_1^2 (2 - x)dx + int_2^5 (x - 2) dx + int_1^3 (3 - x) dx + int_3^5 ( x - 3) dx`
= `[x^2/2 - x]_1^5 + [2x - x^2/2]_1^2 + [x^2/2 - 2x]_2^5 + [3x - x^2/2]_1^3 + [x^2/3 - 3x]_3^5`
= 17
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`
Evaluate : `int1/(3+5cosx)dx`
Evaluate :
`∫_0^π(4x sin x)/(1+cos^2 x) dx`
Evaluate :
`int_e^(e^2) dx/(xlogx)`
Evaluate the integral by using substitution.
`int_0^1 sin^(-1) ((2x)/(1+ x^2)) dx`
Evaluate the integral by using substitution.
`int_0^(pi/2) (sin x)/(1+ cos^2 x) dx`
Evaluate the integral by using substitution.
`int_0^2 dx/(x + 4 - x^2)`
Evaluate the integral by using substitution.
`int_(-1)^1 dx/(x^2 + 2x + 5)`
Evaluate `int_0^(pi/4) (sinx + cosx)/(16 + 9sin2x) dx`
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate of the following integral:
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:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
`int_0^1 x(1 - x)^5 "dx" =` ______.
Evaluate: `int_0^(π/2) sin 2x tan^-1 (sin x) dx`.
Evaluate: `int x/(x^2 + 1)"d"x`
