Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Advertisements
उत्तर
`int sqrt(9 - (2x + 5)^2) "d"x = int sqrt(3^2 - (2x + 5)^2) "d"x`
Put 2x + 5 = t
2 dx = dt
dx = `1/2 "dt"`
= `int sqrt(3^2 - "t"^2) xx 1/2 "dt"`
= `1/2 int sqrt(3^2 - "t"^2) "dt"`
= `1/2 ["t"/2 sqrt(3^2 - "t"^2) + 3^2/2 sin^-1 ("t"/3) + "c"]`
= `1/4 [(2x + 5) sqrt(9 - (2x + 5)^2) + 9 sin^-1 ((2x + 5)/3)] + "c"`
`int sqrt(9 - (2x + 5)^2) "d"x = 1/4 [(2x + 5) sqrt(9 - (2x + 5)^2) + 9 sin^-1 ((2x + 5)/3)] + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "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 :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
(2x – 5)(3x + 4x)
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`(1 + cos 4x)/(cos x - tan x)`
Integrate the following functions with respect to x :
`(x + 1)/((x + 2)(x + 3))`
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 :
`cot x/(log(sin x))`
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:
x log x
Integrate the following with respect to x:
`tan^-1 ((8x)/(1 - 16x^2))`
Integrate the following with respect to x:\
`logx/(1 + log)^2`
Find the integrals of the following:
`1/((x + 1)^2 - 25)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Choose the correct alternative:
`int ("e"^x (1 + x))/(cos^2(x"e"^x)) "d"x` is
Choose the correct alternative:
`int (x + 2)/sqrt(x^2 - 1) "d"x` is
Choose the correct alternative:
`int sin sqrt(x) "d"x` is
