Advertisements
Advertisements
प्रश्न
Evaluate the following integrals using properties of integration:
`int_0^1 |5x - 3| "d"x`
उत्तर
f(x) = |5x – 3| = `{{:(-(5x - 3), "if" x < 3/5),(5x - 3, "if" x ≥ 3/5):}`
I = `int_0^1 |5x - 3| "d"x`
= `int_0^1 (3 - 5x) "d"x + int_(3/5)^1 (5x - 3) "d"x`
= `[3x - (5x^2)/2]_0^(3/5) + ](5x^2)/2 - 3x]_(3/5)^1`
= `9/5 - 9/10 + 5/2 - 3 - 9/10 + 9/5`
= `18/5 - 18/10 + 5/2 - 3`
= `9/5 + 5/2 - 3`
= `(18 + 25 - 30)/10`
= `13/10`
APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals:
`int_3^4 (d"x)/(x^2 - 4)`
Evaluate the following definite integrals:
`int_(-1)^1 ("d"x)/(x^2 + 2x + 5)`
Evaluate the following definite integrals:
`int_0^1 sqrt((1 - x)/(1 + x)) "d"x`
Evaluate the following definite integrals:
`int_0^1 (1 - x^2)/(1 + x^2)^2 "d"x`
Evaluate the following integrals using properties of integration:
`int_(-5)^5 x cos(("e"^x - 1)/("e"^x + 1)) "d"x`
Evaluate the following integrals using properties of integration:
`int_(- pi/4)^(pi/4) sin^2x "d"x`
Evaluate the following integrals using properties of integration:
`int_0^(2pi) x log((3 + cosx)/(3 - cosx)) "d"x`
Evaluate the following integrals using properties of integration:
`int_0^pi sin^4 x cos^3 x "d"x`
Evaluate the following integrals using properties of integration:
`int_0^1 (log(1 + x))/(1 + x^2) "d"x`
Evaluate the following integrals using properties of integration:
`int_(pi/8)^((3pi)/8) 1/(1 + sqrt(tan x)) "d"x`
Evaluate the following integrals using properties of integration:
`int_0^pi x[sin^2(sin x) cos^2 (cos x)] "d"x`
Choose the correct alternative:
For any value of n ∈ Z, `int_0^pi "e"^(cos^2x) cos^3[(2n+ 1)x] "d"x` is
Choose the correct alternative:
The value of `int_(- pi/2)^(pi/2) sin^2x cos x "d"x` is
Choose the correct alternative:
The value of `int_(-4)^4 [tan^-1 ((x^2)/(x^4 + 1)) + tan^-1 ((x^4 + 1)/x^2)] "d"x` is
Choose the correct alternative:
The value of `int_(- pi/4)^(pi/4) ((2x^7 - 3x^5 + 7x^3 - x + 1)/(cos^2x)) "d"x` is
Choose the correct alternative:
The value of `int_0^pi ("d"x)/(1 + 5^(cosx))` is
