Advertisements
Advertisements
प्रश्न
Evaluate the definite integral:
`int_2^3 dx/(x^2 - 1)`
Advertisements
उत्तर
`int_2^3 dx/ (x^2 - 1)`
`= [1/2 log ((x - 1)/ (x + 1))]_2^3`
`= 1/2 [log ((3-1)/(3 + 1)) - log ((2 - 1)/(2+1))]`
`= 1/2 [log (2/4) - log (1/3)]`
`= 1/2 log ((2/4)/ (1/3))`
`= 1/2 log 3/2`
APPEARS IN
संबंधित प्रश्न
If `int_0^h1/(2+8x^2)dx=pi/16 `then find the value of h.
Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)dx`
Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(cosx))dx`
Evaluate the definite integral:
`int_(-1)^1 (x + 1)dx`
Evaluate the definite integral:
`int_2^3 1/x dx`
Evaluate the definite integral:
`int_1^2 (4x^3 - 5x^2 + 6x + 9) dx`
Evaluate the definite integral:
`int_0^(pi/2) cos 2x dx`
Evaluate the definite integral:
`int_4^5 e^x dx`
Evaluate the definite integral:
`int_0^(pi/4) tan x dx`
Evaluate the definite integral:
`int_0^1 dx/sqrt(1-x^2)`
Evaluate the definite integral:
`int_0^(pi/2) cos^2 xdx`
Evaluate the definite integral:
`int_2^3 (xdx)/(x^2 + 1)`
Evaluate the definite integral:
`int_0^1 (2x + 3)/(5x^2 + 1) dx`
Evaluate the definite integral:
`int_0^1 x e^(x^2) dx`
Evaluate the definite integral:
`int_1^2 (5x^2)/(x^2 + 4x + 3)`
Evaluate the definite integral:
`int_0^(pi/4) (2 sec^2 x + x^3 + 2) dx`
Evaluate the definite integral:
`int_0^pi (sin^2 x/2 - cos^2 x/2) dx`
Evaluate the definite integral:
`int_0^1 (xe^x + sin (pix)/4)`
`int_1^(sqrt3)dx/(1+x^2) ` equals:
Evaluate : \[\int\frac{x \cos^{- 1} x}{\sqrt{1 - x^2}}dx\] .
`int_6^(2/3) (dx)/(4 + 9x^2)` equals
Evaluate:
`int_0^π(sin^4x + cos^4x)dx`
Hence evaluate:
`int_(-2π)^(2π) (sin^4x + cos^4x)/(1 + e^x)dx`
If \(f\) is continuous on \([a,b]\) and \[A(x)=\int_a^x f(t)\,dt,\] what is \(A'(x)\) for every \(x\) in \((a,b)\)?
Which expression correctly applies the limits to a definite integral?
Under the substitution \[30-x^{\frac32}=t,\] what is the correct expression for \(\sqrt{x}\,dx\)?
An antiderivative of \[\frac{\sqrt{x}}{(30-x^{\frac32})^2}\] is:
Evaluate \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx.\]
