Advertisements
Advertisements
Question
Fill in the blank : `int_(-2)^3 dx/(x + 5)` = _______
Solution
Let I = `int_(-2)^3 dx/(x + 5)*dx`
= `[log |x + 5|]_(-2)^3`
= [log |3 + 5| – log |–2 + 5|]
= log 8 – log 3
∴ I = `log(8/3)`.
APPEARS IN
RELATED QUESTIONS
Evaluate the following:
`int_0^(pi/2) log(tanx)dx`
Evaluate the following : `int_(-a)^(a) (x + x^3)/(16 - x^2)*dx`
Evaluate the following : `int_0^1 (logx)/sqrt(1 - x^2)*dx`
Evaluate the following : `int_(pi/4)^(pi/2) (cos theta)/[cos theta/2 + sin theta/2]^3*d theta`
Evaluate the following : `int_0^(pi/4) (tan^3x)/(1 +cos2x)*dx`
Evaluate the following : `int_0^pi x*sinx*cos^4x*dx`
Evaluate the following : `int_0^(pi/2) [2 log (sinx) - log (sin 2x)]*dx`
Evaluate the following : `int_0^pi (sin^-1x + cos^-1x)^3 sin^3x*dx`
Evaluate the following definite integrals: If `int_0^"a" (2x + 1)*dx` = 2, find the real value of a.
Evaluate the following definite integral:
`int_1^3 logx.dx`
Evaluate the following integrals : `int_0^"a" x^2("a" - x)^(3/2)*dx`
Choose the correct alternative :
`int_2^3 x/(x^2 - 1)*dx` =
Solve the following:
`int_0^1 e^(x^2)*x^3dx`
Solve the following : `int_2^4 x/(x^2 + 1)*dx`
Choose the correct alternative:
`int_2^3 x/(x^2 - 1) "d"x` =
`int_2^3 "x"/("x"^2 - 1)` dx = ____________.
Evaluate the following integrals:
`int_-9^9 (x^3)/(4 - x^2) dx`
`int_0^4 1/sqrt(4x - x^2)dx` = ______.
Evaluate the following definite intergral:
`int_-2^3 1/(x+5) · dx`
Evaluate the following definite intergral:
`int_1^2(3x)/(9x^2-1).dx`
