Advertisements
Advertisements
प्रश्न
Evaluate `∫_0^(3/2)|x cosπx|dx`
Advertisements
उत्तर
`int_0^(3/2)|xcospix|dx`
`0<x<1/2`
`0<pix<pi/2rArrcospix>0rArr(xcospix)>0`
`|xcospix|=xcospix`
`1/2<x<3/2`
`pi/2<pix<(3pi)/2rArrcospix<0rArr(xcospix)<0`
`|xcospix|=-xcospix`
`I=int_0^(3/2)|xcospix|dx=int_0^(3/2)xcospix+int_(1/2)^(3/2)-(xcospix)`
`I=int_0^(1/2)xcospix-int_(1/2)^(3/2)xcospix`
`intx(cospix)=x(sinpix)/pi-int(sinpix)/pi`
`=x/pi(sinpix)+(cospix)/pi^2`
`I=[(x/pisinpix)+(cospix)/pi^2]_0^(1/2)-[(x/pisinpix)+(cospix)/pi^2]_(1/2)^(3/2)`
`=[1/pi((1/2)-0)+1/pi^2(0-1)]-[1/pi(3/2(-1)-1/2(1))+1/pi^2(0-0)]`
`=(1/(2pi)-1/pi^2)-((-2)/pi)`
`=(5/(2pi)-1/pi^2)`
`=((5pi-2)/(2pi^2))`
संबंधित प्रश्न
Evaluate: `int1/(xlogxlog(logx))dx`
Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`
find `∫_2^4 x/(x^2 + 1)dx`
Evaluate the integral by using substitution.
`int_0^(pi/2) (sin x)/(1+ cos^2 x) dx`
Evaluate of the following integral:
Evaluate of the following integral:
Evaluate :
Evaluate the following definite integral:
Evaluate the following integral:
Evaluate each of the following integral:
Evaluate each of the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate the following integral:
Evaluate
\[\int\limits_0^\pi \frac{x}{1 + \sin \alpha \sin x}dx\]
Evaluate the following integral:
Evaluate :
Evaluate: `int_ e^x ((2+sin2x))/cos^2 x dx`
Evaluate: `int_-1^2 (|"x"|)/"x"d"x"`.
Find: `int_ (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.
`int_0^3 1/sqrt(3x - x^2)"d"x` = ______.
`int_0^(pi4) sec^4x "d"x` = ______.
Which limits are used to evaluate the resulting expression in Method: Resubstitution?
After using \[t=\tan^{-1}x\] in \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\], which integral results?
What is the value of \[\int_{0}^{1}\frac{\tan^{-1}x}{1+x^2}\,dx\]?
