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
Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`
Integrate the functions:
`x/(e^(x^2))`
Write a value of
Write a value of
Integrate the following w.r.t. x : `int x^2(1 - 2/x)^2 dx`
Evaluate the following integrals : `int (cos2x)/(sin^2x.cos^2x)dx`
Integrate the following functions w.r.t. x : `e^x.log (sin e^x)/tan(e^x)`
Integrate the following functions w.r.t. x : cos7x
Evaluate the following : `int (1)/(4x^2 - 3).dx`
Evaluate the following:
`int (1)/(25 - 9x^2)*dx`
Evaluate the following : `int (1)/sqrt(3x^2 - 8).dx`
Evaluate the following : `int (1)/(x^2 + 8x + 12).dx`
Evaluate the following integrals : `int (3x + 4)/(x^2 + 6x + 5).dx`
Evaluate the following integrals : `int sqrt((x - 7)/(x - 9)).dx`
Evaluate the following.
`int ("e"^"x" + "e"^(- "x"))^2 ("e"^"x" - "e"^(-"x"))`dx
State whether the following statement is True or False.
The proper substitution for `int x(x^x)^x (2log x + 1) "d"x` is `(x^x)^x` = t
Evaluate `int "x - 1"/sqrt("x + 4")` dx
Evaluate `int"e"^x (1/x - 1/x^2) "d"x`
`int sec^6 x tan x "d"x` = ______.
`int(7x - 2)^2dx = (7x -2)^3/21 + c`
Evaluate the following.
`int x^3/(sqrt(1+x^4))dx`
Evaluate `int(1+ x + x^2/(2!)) dx`
If f′(x) = 4x3 − 3x2 + 2x + k, f(0) = -1 and f(1) = 4, find f(x)
Evaluate the following.
`int (x^3)/(sqrt(1 + x^4)) dx`
Evaluate the following.
`int1/(x^2 + 4x - 5) dx`
Evaluate `int(1 + x + x^2 / (2!))dx`
If f'(x) = 4x3 - 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
If f'(x) = 4x3 – 3x2 + 2x + k, f(0) = 1 and f(1) = 4, find f(x).
