Advertisements
Advertisements
प्रश्न
Evaluate the following definite integrals:
`int_3^4 (d"x)/(x^2 - 4)`
उत्तर
Let I = `int_3^4 (d"x)/(x^2 - 4)`
= `int_3^4 ("d"x)/(x^2 - 2^2)` ......`[because ("d"x)/(x^2 - 2^2) = 1/(2"a") log((x - "a")/(x "a"))]`
= `[1/(2(2)) log((x - 2)/(x + 2))]_3^4`
= `1/4[log(2/6) - log(1/5)]`
= `1/4[log(2/6 xx 5/1)]`
= `1/4 log (5/3)`
APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals:
`int_0^1 sqrt((1 - x)/(1 + x)) "d"x`
Evaluate the following definite integrals:
`int_0^(pi/2) "e"^x((1 + sin x)/(1 + cos x))"d"x`
Evaluate the following definite integrals:
`int_0^(pi/2) sqrt(cos theta) sin^3theta "d"theta`
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/2)^(pi/2) (x^5 + x cos x + tan^3 x + 1) "d"x`
Evaluate the following integrals using properties of integration:
`int_0^(sin^2x) sin^-1 sqrt("t") "dt" + int_0^(cos^2x) cos^-1 sqrt("t") "dt"`
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_0^pi(xsinx)/(1 + sinx) "'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:
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_0^pi ("d"x)/(1 + 5^(cosx))` is
