Advertisements
Advertisements
प्रश्न
Evaluate the definite integral:
`int_0^1 dx/sqrt(1-x^2)`
Advertisements
उत्तर
`int_0^1 dx/sqrt(1 - x^2)`
`= [sin^-1 x]_0^1`
`= sin^-1 (1) - sin^-1 0`
= `pi/2 - 0`
`= pi/2`
APPEARS IN
संबंधित प्रश्न
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_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_2^3 dx/(x^2 - 1)`
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_0^(pi/4) (2 sec^2 x + x^3 + 2) dx`
Evaluate the definite integral:
`int_0^1 (xe^x + sin (pix)/4)`
`int_0^(2/3) dx/(4+9x^2)` equals:
`int_1^sqrt(3) (dx)/(1 + x^2)` equals
`int_6^(2/3) (dx)/(4 + 9x^2)` equals
Hence evaluate:
`int_(-2π)^(2π) (sin^4x + cos^4x)/(1 + e^x)dx`
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?
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:
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?
Which function is an antiderivative of \[\sin^3 2t\cos 2t?\]
Evaluate \[\int_0^{\frac\pi4}\sin^3 2t\cos 2t\,dt.\]
