Advertisements
Advertisements
प्रश्न
Using second fundamental theorem, evaluate the following:
`int_0^1 "e"^(2x) "d"x`
बेरीज
उत्तर
`int_0^1 "e"^(2x) "d"x = ["e"^(2x)/2]_0^1`
= `1/2 ["e"^(2x)]_0^1`
= `1/2["e"^(2(1)) - "e"^(2(0))]`
= `1/2 ["e"^2 - "e"^0]`
= `1/2 ["e"^2 - 1]`
shaalaa.com
Definite Integrals
या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
APPEARS IN
संबंधित प्रश्न
\[\int_\frac{\pi}{6}^\frac{\pi}{3} \left( \tan x + \cot x \right)^2 dx\]
\[\int\limits_0^\pi \frac{1}{5 + 3 \cos x} dx\]
\[\int\limits_0^\pi \log\left( 1 - \cos x \right) dx\]
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
\[\int\limits_0^{15} \left[ x \right] dx .\]
\[\int\limits_0^{\pi/4} \sin 2x \sin 3x dx\]
\[\int\limits_0^{2\pi} \cos^7 x dx\]
Using second fundamental theorem, evaluate the following:
`int_0^3 ("e"^x "d"x)/(1 + "e"^x)`
Choose the correct alternative:
`int_0^oo x^4"e"^-x "d"x` is
`int (x + 3)/(x + 4)^2 "e"^x "d"x` = ______.
