Advertisements
Advertisements
प्रश्न
Solve the following : `int_(-2)^3 (1)/(x + 5)*dx`
उत्तर
Let I = `int_(-2)^3 (1)/(x + 5)*dx`
= `[log |x + 5|]_(-2)^3`
= [log |3 + 5| – log |–2 + 5|]
= log 8 – log 3
∴ I = `log(8/3)`.
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^(pi/4) (sec^2x)/(3tan^2x + 4tan x +1)*dx`
`int_2^3 dx/(x(x^3 - 1))` = ______.
Evaluate the following : `int_0^(pi/2) 1/(6 - cosx)*dx`
Evaluate the following definite integrals: `int_1^2 dx/(x^2 + 6x + 5)`
Evaluate the following integrals : `int_0^1 log(1/x - 1)*dx`
Choose the correct alternative :
`int_(-7)^7 x^3/(x^2 + 7)*dx` =
Fill in the blank : `int_0^1 dx/(2x + 5)` = _______
State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_(-"b")^(-"a") f(x)*dx`
Solve the following : `int_1^2 (x + 3)/(x (x + 2))*dx`
Solve the following : `int_0^1 (x^2 + 3x + 2)/sqrt(x)*dx`
Solve the following : `int_2^3 x/(x^2 + 1)*dx`
Prove that: `int_0^(2"a") "f"(x) "d"x = int_0^"a" "f"(x) "d"x + int_0^"a" "f"(2"a" - x) "d"x`
Evaluate `int_1^"e" 1/(x(1 + log x)^2) "d"x`
Evaluate `int_1^2 "e"^(2x) (1/x - 1/(2x^2)) "d"x`
By completing the following activity, Evaluate `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Solution: Let I = `int_1^2 (x + 3)/(x(x + 2)) "d"x`
Let `(x + 3)/(x(x + 2)) = "A"/x + "B"/((x + 2))`
∴ x + 3 = A(x + 2) + B.x
∴ A = `square`, B = `square`
∴ I = `int_1^2[("( )")/x + ("( )")/((x + 2))] "d"x`
∴ I = `[square log x + square log(x + 2)]_1^2`
∴ I = `square`
Evaluate the following definite intergral:
`int_-2^3 1/(x+5) dx`
Solve the following.
`int_1^3 x^2 log x dx `
Evaluate the following definite integral:
`int_1^3 logx.dx`
Evaluate the following definite intergral:
`int_(-2)^3 1/(x + 5)dx`
Evaluate the following definite intergral:
`int_(1)^3logx dx`