Advertisements
Advertisements
प्रश्न
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Advertisements
उत्तर
`int 1/sqrt(9 + 8x - x^2) "d"x = int ("d"x)/sqrt(9 - (x^2 - 8x))`
= `int ("d"x)/sqrt(9 - [(x - 4)^2 - 4^2]`
= `int ("d"x)/sqrt(9 - [(x - 4)^2 - 16]`
= `int ("d"x)/sqrt(9 - (x - 4)^2 + 16)`
= `int ("d"x)/sqrt(25 - (x - 4)^2`
= `int ("d"x)/sqrt(5^2 - (x - 4)^2`
Put x – 4 = t
dx = dt
`int ("d")/sqrt(9 + 8x - x^2) = int ("d"x)/sqrt(5^2 - "t"^2)`
`int ("d"x)/sqrt("a"^2 - x^2) = sin^-1 (x/"a") + "c"`
`int ("d"x)/sqrt(9 + 8x - x^2) = sin^-1 ("t"/5) + "c"`
= `sin^-1 ((x - 4)/5) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int1/(x(3+logx))dx`
Evaluate : `int (1+logx)/(x(2+logx)(3+logx))dx`
Evaluate:`int(tansqrtx)/sqrtxdx`
Find the volume of the solid obtained by revolving about the X-axis, the region bounded by the curve `"x"^2/4 - "y"^2/9 = 1` and the lines x = 2 , x = 4.
Integrate the following functions with respect to x :
`(sin4x)/sinx`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(10x^9 + 10^x log_"e" 10)/(10^x + x^10)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(- 4x) sin 2x`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/(9x^2 - 4)`
Integrate the following with respect to x:
`(5x - 2)/(2 + 2x + x^2)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Choose the correct alternative:
`int sin^2x "d"x` is
Choose the correct alternative:
`int ("d"x)/("e"^x - 1)` is
Choose the correct alternative:
`int "e"^(sqrt(x)) "d"x` is
