Advertisements
Advertisements
प्रश्न
Evaluate `int_-a^a f(x) dx`, where f(x) = `9^x/(1 + 9^x)`.
Advertisements
उत्तर
`int_-a^a 9^x/(1 + 9^x)dx`
Let 1 + 9x = u
On differentiating with respect to x.
`\implies` 9x . log 9 = `(du)/dx`
`\implies` 9x dx = `(du)/log9`
= `int_(1 + 9^-a)^(1 + 9^a) (du)/(log9.u)`
= `1/log9 . [log (u)]_(1 + 9^-a)^(1 + 9^a) + C`
= `1/log9 [log (1 + 9^a) - log (1 + 9^-a)] + C`
= `1/log9 [log ((1 + 9^a)/(1 + 9^-a))] + C`.
APPEARS IN
संबंधित प्रश्न
Integrate the functions:
`xsqrt(1+ 2x^2)`
Integrate the functions:
`sqrt(sin 2x) cos 2x`
`int (dx)/(sin^2 x cos^2 x)` equals:
Evaluate: `int_0^3 f(x)dx` where f(x) = `{(cos 2x, 0<= x <= pi/2),(3, pi/2 <= x <= 3) :}`
Write a value of
Evaluate the following integrals: `int sin 4x cos 3x dx`
Evaluate the following integrals:
`int x/(x + 2).dx`
Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`
If `f'(x) = x - (3)/x^3, f(1) = (11)/(2)`, find f(x)
Integrate the following functions w.r.t. x : `(7 + 4 + 5x^2)/(2x + 3)^(3/2)`
Integrate the following functions w.r.t. x:
`(sinx cos^3x)/(1 + cos^2x)`
Evaluate the following : `(1)/(4x^2 - 20x + 17)`
Evaluate the following integrals:
`int (7x + 3)/sqrt(3 + 2x - x^2).dx`
Integrate the following with respect to the respective variable:
`x^7/(x + 1)`
Evaluate the following.
`int (2"e"^"x" + 5)/(2"e"^"x" + 1)`dx
State whether the following statement is True or False.
If `int x "e"^(2x)` dx is equal to `"e"^(2x)` f(x) + c, where c is constant of integration, then f(x) is `(2x - 1)/2`.
`int sqrt(1 + sin2x) dx`
To find the value of `int ((1 + logx))/x` dx the proper substitution is ______
`int sec^6 x tan x "d"x` = ______.
`int ("d"x)/(x(x^4 + 1))` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
The value of `sqrt(2) int (sinx dx)/(sin(x - π/4))` is ______.
Find `int (x + 2)/sqrt(x^2 - 4x - 5) dx`.
Evaluate `int(1 + x + x^2/(2!))dx`
Evaluate the following.
`int x sqrt(1 + x^2) dx`
Evaluate:
`int(sqrt(tanx) + sqrt(cotx))dx`
Evaluate the following.
`intx^3/sqrt(1 + x^4) dx`
What is integration by substitution?
