Advertisements
Advertisements
प्रश्न
Integrate the following functions with respect to x :
`(3x + 4) sqrt(3x + 7)`
उत्तर
`int (3x + 4) sqrt(3x + 7) "d"x = int (3x + 7 - 3) sqrt(3x + 7) "d"x`
= `int [(3x + 7) sqrt(3x + 7) - 3sqrt(3x + 7)] "d"x`
= `int (3x + 7) sqrt(3x + 7) "d"x - int 3sqrt(3x + 7) "d"x`
= `int (3x + 7)^(3/2) "d"x - 3int (3x + 7)^(1/2) "d"x`
= `1/3 (3x + 7)^(3/2 + 1)/(3/2 + 1) - 3(3x + 7)^(1/2 + 1)/(1/2 + 1) + "c"`
= `1/3 (3x + 7)^(5/2)/(5/2) - 3 xx 1/3 (3x + 7)^(3/2)/(3/2) + "c"`
= `1/3 xx 2/5 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
= `2/15 (3x + 7)^(5/2) - 2/3 (3x + 7)^(3/2) + "c"`
APPEARS IN
संबंधित प्रश्न
Evaluate : `int_0^1 "x" . "tan"^-1 "x" "dx"`
Find the elasticity of demand if the marginal revenue is ₹ 50 and price is ₹ 75.
Integrate the following functions with respect to x :
`(sin^2x)/(1 + cosx)`
Integrate the following with respect to x :
`x/sqrt(1 + x^2)`
Integrate the following with respect to x :
`("cosec" x)/(log(tan x/2))`
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
x3 sin x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`"e"^("a"x) cos"b"x`
Integrate the following with respect to x:
`"e"^(2x) sinx`
Integrate the following with respect to x:
`"e"^x (tan x + log sec x)`
Find the integrals of the following:
`1/(25 - 4x^2)`
Find the integrals of the following:
`1/sqrt(x^2 - 4x + 5)`
Integrate the following with respect to x:
`(2x + 1)/sqrt(9 + 4x - x^2)`
Integrate the following functions with respect to x:
`sqrt(9 - (2x + 5)^2`
Choose the correct alternative:
`int 2^(3x + 5) "d"x` is
Choose the correct alternative:
`int (x^2 + cos^2x)/(x^2 + 1) "cosec"^2 x/("d"x)` is
Choose the correct alternative:
`int sqrt((1 - x)/(1 + x)) "d"x` is
