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
Find the volume of solid generated by rotating the area bounded by x2+y2 =36 and the lines x = 0, x = 3 about X -axis.
Evaluate:`int(tansqrtx)/sqrtxdx`
Integrate the following functions with respect to x :
`(cos2x - cos 2 alpha)/(cosx - cos alpha)`
Integrate the following functions with respect to x :
sin2 5x
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
x5ex2
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Integrate the following with respect to x:
`"e"^(- 3x) cos x`
Find the integrals of the following:
`1/(4 - x^2)`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt(xx^2 + 4x + 2)`
Integrate the following with respect to x:
`(2x - 3)/(x^2 + 4x - 12)`
Integrate the following with respect to x:
`(3x + 1)/(2x^2 - 2x + 3)`
Integrate the following functions with respect to x:
`sqrt(x^2 - 2x - 3)`
Integrate the following functions with respect to x:
`sqrt((6 - x)(x - 4))`
Integrate the following functions with respect to x:
`sqrt(81 + (2x + 1)^2`
Choose the correct alternative:
`int 1/(x sqrt(log x)^2 - 5) "d"x` is
