Advertisements
Advertisements
प्रश्न
`int_1^2 1/(2x + 3) dx` = ______
उत्तर
`int_1^2 1/(2x + 3) dx` = `bbunderline(1/2 log(7/5))`
APPEARS IN
संबंधित प्रश्न
Prove that: `int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx`
Evaluate :`int_0^pi(xsinx)/(1+sinx)dx`
Evaluate : `intlogx/(1+logx)^2dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(pi/2) cos^2 x dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^2 xsqrt(2 -x)dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^(2x) cos^5 xdx`
By using the properties of the definite integral, evaluate the integral:
`int_0^pi log(1+ cos x) dx`
By using the properties of the definite integral, evaluate the integral:
`int_0^a sqrtx/(sqrtx + sqrt(a-x)) dx`
Evaluate the definite integrals `int_0^pi (x tan x)/(sec x + tan x)dx`
Evaluate : \[\int(3x - 2) \sqrt{x^2 + x + 1}dx\] .
Evaluate : `int _0^(pi/2) "sin"^ 2 "x" "dx"`
Prove that `int _a^b f(x) dx = int_a^b f (a + b -x ) dx` and hence evaluate `int_(pi/6)^(pi/3) (dx)/(1 + sqrt(tan x))` .
`int_0^1 "e"^(2x) "d"x` = ______
Evaluate `int_0^1 x(1 - x)^5 "d"x`
`int_0^{pi/2} log(tanx)dx` = ______
`int_2^3 x/(x^2 - 1)` dx = ______
`int_0^1 (1 - x)^5`dx = ______.
If `int_0^"a" sqrt("a - x"/x) "dx" = "K"/2`, then K = ______.
`int_3^9 x^3/((12 - x)^3 + x^3)` dx = ______
If f(x) = |x - 2|, then `int_-2^3 f(x) dx` is ______
`int_0^pi sin^2x.cos^2x dx` = ______
`int_0^pi x*sin x*cos^4x "d"x` = ______.
`int_0^1 1/(2x + 5) dx` = ______.
If `int_a^b x^3 dx` = 0, then `(x^4/square)_a^b` = 0
⇒ `1/4 (square - square)` = 0
⇒ b4 – `square` = 0
⇒ (b2 – a2)(`square` + `square`) = 0
⇒ b2 – `square` = 0 as a2 + b2 ≠ 0
⇒ b = ± `square`
If `intxf(x)dx = (f(x))/2` then f(x) = ex.
If `β + 2int_0^1x^2e^(-x^2)dx = int_0^1e^(-x^2)dx`, then the value of β is ______.
Let `int ((x^6 - 4)dx)/((x^6 + 2)^(1/4).x^4) = (ℓ(x^6 + 2)^m)/x^n + C`, then `n/(ℓm)` is equal to ______.
The value of the integral `int_0^sqrt(2)([sqrt(2 - x^2)] + 2x)dx` (where [.] denotes greatest integer function) is ______.
With the usual notation `int_1^2 ([x^2] - [x]^2)dx` is equal to ______.
`int_(π/3)^(π/2) x sin(π[x] - x)dx` is equal to ______.
Evaluate: `int_(-π//4)^(π//4) (cos 2x)/(1 + cos 2x)dx`.
Evaluate the following definite integral:
`int_-2^3 1/(x + 5) dx`
Evaluate the following integral:
`int_0^1x (1 - x)^5 dx`
Evaluate the following integral:
`int_0^1 x(1 - x)^5 dx`
Evaluate the following definite integral:
`int_-2^3(1)/(x + 5) dx`