Advertisements
Advertisements
Question
Evaluate `int_1^2 (3x)/((9x^2 - 1)) "d"x`
Solution
Let I = `int_1^2 (3x)/((9x^2 - 1)) "d"x`
= `3int_1^2 x/(9x^2 - 1) "d"x`
Put 9x2 – 1 = t
∴ 18x dx = dt
∴ x dx = `1/18` dt
When x = 1, t = 9(1)2 – 1 = 8
When x = 2, t = 9(2)2 – 1 = 35
∴ I = `3int_8^35 1/"t"*"dt"/18`
= `1/6 int_8^35 "dt"/"t"`
= `1/6[log|"t"|]_8^35`
= `1/6(log 35 - log 8)`
∴ I = `1/6 log (35/8)`
APPEARS IN
RELATED QUESTIONS
Evaluate : `int_0^(pi/4) (sec^2x)/(3tan^2x + 4tan x +1)*dx`
Evaluate : `int_0^(pi//4) (sin2x)/(sin^4x + cos^4x)*dx`
Evaluate : `int_0^(pi/2) (1)/(5 + 4 cos x)*dx`
Evaluate : `int_1^3 (cos(logx))/x*dx`
Evaluate the following : `int_((-pi)/4)^(pi/4) (x + pi/4)/(2 - cos 2x)*dx`
Choose the correct option from the given alternatives :
`int_0^9 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx` =
Evaluate the following : `int_0^1 sin^-1 ((2x)/(1 + x^2))*dx`
Evaluate the following : `int_0^pi (sin^-1x + cos^-1x)^3 sin^3x*dx`
Choose the correct alternative :
`int_2^7 sqrt(x)/(sqrt(x) + sqrt(9 - x))*dx` =
State whether the following is True or False : `int_"a"^"b" f(x)*dx = int_"a"^"b" f(x - "a" - "b")*dx`
State whether the following is True or False : `int_4^7 ((11 - x)^2)/((11 - x)^2 + x^2)*dx = (3)/(2)`
Solve the following : `int_2^4 x/(x^2 + 1)*dx`
Evaluate `int_2^3 x/((x + 2)(x + 3)) "d"x`
`int_(-2)^2 sqrt((2 - x)/(2 + x))` = ?
`int_0^1 tan^-1 ((2x - 1)/(1 + x - x^2))` dx = ?
Evaluate the following definite intergral:
`int_1^3 log xdx`
If `int_((-pi)/4) ^(pi/4) x^3 * sin^4 x dx` = k then k = ______.
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`
Evaluate the following definite integral:
`int_1^2 (3x)/((9x^2 - 1))*dx`
