Advertisements
Advertisements
प्रश्न
Evaluate the definite integral:
`int_0^1 dx/(1+x^2)`
Advertisements
उत्तर
`int_0^1 dx/(1 + x^2)`
`= [tan^-1 x]_0^1`
`= tan^-1 (1) - tan^-1 0`
`= pi/4 - 0`
`= pi/4`
APPEARS IN
संबंधित प्रश्न
If `int_0^h1/(2+8x^2)dx=pi/16 `then find the value of h.
Evaluate :`int_0^(pi/2)(2^(sinx))/(2^(sinx)+2^(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_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 dx/(x^2 - 1)`
Evaluate the definite integral:
`int_0^(pi/2) cos^2 xdx`
Evaluate the definite integral:
`int_0^1 (2x + 3)/(5x^2 + 1) dx`
Evaluate the definite integral:
`int_1^2 (5x^2)/(x^2 + 4x + 3)`
Evaluate the definite integral:
`int_0^pi (sin^2 x/2 - cos^2 x/2) dx`
`int_1^(sqrt3)dx/(1+x^2) ` equals:
Evaluate : \[\int\frac{x \cos^{- 1} x}{\sqrt{1 - x^2}}dx\] .
`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`
Hence evaluate:
`int_(-2π)^(2π) (sin^4x + cos^4x)/(1 + e^x)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?
Under the substitution \[30-x^{\frac32}=t,\] what is the correct expression for \(\sqrt{x}\,dx\)?
Which function is an antiderivative of \[\sin^3 2t\cos 2t?\]
Evaluate \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt.\]
