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
Definite Integrals
क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
APPEARS IN
संबंधित प्रश्न
\[\int\limits_{- \pi/4}^{\pi/4} \frac{1}{1 + \sin x} dx\]
\[\int\limits_0^\pi \frac{1}{5 + 3 \cos x} dx\]
\[\int\limits_0^{\pi/2} \frac{\sqrt{\cot x}}{\sqrt{\cot x} + \sqrt{\tan x}} dx\]
\[\int\limits_0^\pi x \log \sin x\ dx\]
\[\int\limits_0^\pi \frac{x \sin x}{1 + \sin x} dx\]
\[\int\limits_1^4 \left( x^2 - x \right) dx\]
\[\int\limits_1^3 \left( 2 x^2 + 5x \right) dx\]
\[\int\limits_0^\infty \frac{1}{1 + e^x} dx\] equals
\[\int\limits_0^{2a} f\left( x \right) dx\] is equal to
Using second fundamental theorem, evaluate the following:
`int_0^1 "e"^(2x) "d"x`
