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`
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Integrate the following functions with respect to x :
`(x^3 + 4x^2 - 3x + 2)/x^2`
Integrate the following functions with respect to x :
`(cos 2x)/(sin^2x cos^2x)`
Integrate the following with respect to x :
`x^2/(1 + x^6)`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`(sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x :
`1/(x log x log (log x))`
Integrate the following with respect to x :
sin5x cos3x
Integrate the following with respect to x:
9xe3x
Integrate the following with respect to x:
x sin 3x
Integrate the following with respect to x:
25xe–5x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:
`"e"^x ((x - 1)/(2x^2))`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following with respect to x:
`(2x + 3)/sqrt(x^2 + 4x + 1)`
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
