If f x - a x t 3 e t dt- then d - dx f x - MP PET 1989-A- exx3-3 x2B- x3 ezC- None of theseD- a3 ec

The correct option is B f(x)=∫_a^x t^3 e^t dt=∫_a^0 t^3 . e^t dt + ∫_0^x t^3 e^t dt ⇒df(x)/dx=d/dx ( ∫_a^0 t^3.e^t dt )+d/dx ( ∫_0^x t^3 .e^t dt )=x^3e^x ...

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Byju's Answer

Standard XII

Mathematics

Property 5

If f x =∫ a x...

Question

If $f (x) = \int_{a}^{x} t^{3} e^{t} d t, t h e n \frac{d}{d x} f (x) =$ [MP PET 1989]

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None of these

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Solution

The correct option is B

$f (x) = \int_{a}^{x} t^{3} e^{t} d t = \int_{a}^{0} t^{3} . e^{t} d t + \int_{0}^{x} t^{3} e^{t} d t$
$\Rightarrow \frac{d f (x)}{d x} = \frac{d}{d x} (\int_{a}^{0} t^{3} . e^{t} d t) + \frac{d}{d x} (\int_{0}^{x} t^{3} . e^{t} d t) = x^{3} e^{x}$

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If f(x)=∫xa t3et dt, then ddxf(x)= [MP PET 1989]

The correct option is B f(x)=∫xa t3et dt=∫0at3.et dt+∫x0t3etdt ⇒df(x)dx=ddx(∫0a t3.et dt)+ddx(∫x0t3.et dt)=x3ex

If $f (x) = \int_{a}^{x} t^{3} e^{t} d t, t h e n \frac{d}{d x} f (x) =$ [MP PET 1989]

The correct option is B

$f (x) = \int_{a}^{x} t^{3} e^{t} d t = \int_{a}^{0} t^{3} . e^{t} d t + \int_{0}^{x} t^{3} e^{t} d t$
$\Rightarrow \frac{d f (x)}{d x} = \frac{d}{d x} (\int_{a}^{0} t^{3} . e^{t} d t) + \frac{d}{d x} (\int_{0}^{x} t^{3} . e^{t} d t) = x^{3} e^{x}$