Advertisements
Advertisements
प्रश्न
Using second fundamental theorem, evaluate the following:
`int_0^3 ("e"^x "d"x)/(1 + "e"^x)`
योग
Advertisements
उत्तर
`int_0^3 ("e"^x "d"x)/(1 + "e"^x) = {log |1 + "e"x|}_0^3`
= log |1 + e3| – log |1 + e°|
= log |1 + e3| – log |1 + 1|
= log |1 + e3| – log |2|
= `log |(1 + "e"^3)/2|`
shaalaa.com
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\limits_{\pi/3}^{\pi/4} \left( \tan x + \cot x \right)^2 dx\]
\[\int\limits_0^{\pi/6} \cos^{- 3} 2 \theta \sin 2\ \theta\ d\ \theta\]
\[\int\limits_1^2 \left( x^2 - 1 \right) dx\]
\[\int\limits_0^2 \left( x^2 - x \right) dx\]
\[\int\limits_0^{1/\sqrt{3}} \tan^{- 1} \left( \frac{3x - x^3}{1 - 3 x^2} \right) dx\]
\[\int\limits_0^{\pi/3} \frac{\cos x}{3 + 4 \sin x} dx\]
\[\int\limits_1^3 \left| x^2 - 2x \right| dx\]
\[\int\limits_0^4 x dx\]
Choose the correct alternative:
The value of `int_(- pi/2)^(pi/2) cos x "d"x` is
Integrate `((2"a")/sqrt(x) - "b"/x^2 + 3"c"root(3)(x^2))` w.r.t. x
