Advertisements
Advertisements
प्रश्न
Evaluate the definite integral:
`int_(pi/6)^(pi/4) cosec x dx`
Advertisements
उत्तर
`int_(pi/6)^(pi/4) cosec x dx`
`= [log ("cosec" x + cot x)]_(pi/6)^(pi/4)`
`= log ("cosec" pi/4 - "cot" pi/4) - log ("cosec" pi/6 - "cot" pi/6)`
`= log (sqrt2 - 1) - log (2 - sqrt3)`
`= log (sqrt2 - 1)/(2 - sqrt3)`
`because log m/n`
= log m = log n
APPEARS IN
संबंधित प्रश्न
Evaluate : `∫_0^(π/2)(sin^2 x)/(sinx+cosx)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_2^3 dx/(x^2 - 1)`
Evaluate the definite integral:
`int_0^(pi/2) cos^2 xdx`
Evaluate the definite integral:
`int_0^1 x e^(x^2) dx`
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_0^2 (6x +3)/(x^2 + 4)` dx
`int_1^(sqrt3)dx/(1+x^2) ` equals:
`int_1^sqrt(3) (dx)/(1 + x^2)` equals
`int_6^(2/3) (dx)/(4 + 9x^2)` equals
Evaluate:
`int_0^π(sin^4x + cos^4x)dx`
How can a definite integral be evaluated using the Fundamental Theorem of Integral Calculus?
If \(f\) is continuous on an interval, which expression defines the area function?
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?
Which expression correctly applies the limits to 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:
Which function is an antiderivative of \[\sin^3 2t\cos 2t?\]
Evaluate \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt.\]
