-827 e - x dx is equal toA- 15 e3-2 e2B- 3 e3-6 e2C- 15 e 3-6 e 2D- 6 e3-15 e2

The correct option is C 15e^3 6e^2∫_8^27e^√(x)dx Let nbsp; x=t^3 ⇒ dx=3t^2 dt ∫_2^3e^t 3t^2 dt Using integration by parts =3t^2e^t 3∫2te^tdt nbsp; =[3e^t ...

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Byju's Answer

Standard XII

Mathematics

Continuity of a Function

∫827 e √ x dx...

Question

$27 \int 8 e^{\sqrt[3]{x}} d x$ is equal to

15 e^{3} - 2 e^{2}

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3 e^{3} - 6 e^{2}

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6 e^{3} + 15 e^{2}

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15 e^{3} - 6 e^{2}

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Solution

The correct option is D $15 e^{3} - 6 e^{2}$
$27 \int 8 e^{\sqrt[3]{x}} d x$
Let $x = t^{3} \Rightarrow d x = 3 t^{2} d t$
$3 \int 2 e^{t} 3 t^{2} d t$
Using integration by parts
$= 3 t^{2} e^{t} - 3 \int 2 t e^{t} d t$
$= [3 e^{t} t^{2} - 3 e^{t} (2 t) + 6 e^{t}]_{2}^{3} = 3 e^{3} (9 - 6 + 2) - 3 e^{2} (4 - 4 + 2) = 15 e^{3} - 6 e^{2}$

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27∫8e3√xdx is equal to

The correct option is D 15e3−6e227∫8e3√xdx Let x=t3 ⇒dx=3t2dt 3∫2et3t2dt Using integration by parts =3t2et−3∫2tetdt =[3ett2−3et(2t)+6et]32=3e3(9−6+2)−3e2(4−4+2)=15e3−6e2

$27 \int 8 e^{\sqrt[3]{x}} d x$ is equal to