Advertisements
Advertisements
Question
Evaluate the definite integral:
`int_2^3 dx/(x^2 - 1)`
Advertisements
Solution
`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
RELATED QUESTIONS
If `int_0^h1/(2+8x^2)dx=pi/16 `then find the value of h.
Evaluate the definite integral:
`int_0^(pi/2) cos 2x dx`
Evaluate the definite integral:
`int_0^(pi/4) tan x dx`
Evaluate the definite integral:
`int_(pi/6)^(pi/4) cosec x dx`
Evaluate the definite integral:
`int_0^1 dx/sqrt(1-x^2)`
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^(pi/4) (2 sec^2 x + x^3 + 2) dx`
`int_1^(sqrt3)dx/(1+x^2) ` equals:
`int_0^(2/3) dx/(4+9x^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`
What does the Fundamental Theorem of Integral Calculus connect?
How can a definite integral be evaluated using the Fundamental Theorem of Integral Calculus?
What does \[A(x)=\int_a^x f(t)\,dt\] give?
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 condition permits direct use of the First Fundamental Theorem and the Second Fundamental Theorem on \([a,b]\)?
If \(f\) is continuous on \([a,b]\) and \(F\) is any antiderivative of \(f\), which formula evaluates the definite integral?
Why is there no need to write the constant of integration \(C\) while evaluating a definite integral?
For \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx,\] which substitution is used?
An antiderivative of \[\frac{\sqrt{x}}{(30-x^{\frac32})^2}\] is:
Evaluate \[\int_4^9\frac{\sqrt{x}}{(30-x^{\frac32})^2}\,dx.\]
For \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt,\] which substitution and differential relation are correct?
Evaluate \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt.\]
