The value of - ax - exdx is equal to- where a - 0 and a 1where C is integration constant

Name: JEE- Grade 12- Mathematics- Indefinite Integrals- Session 02- W07
Uploaded: 2022-07-04T10:36:42+05:30
Description: ∫ a^x · e^xdx =∫ (ae)^xdx {∵∫ a^x dx= a^xln a+C nbsp; } =(ae)^xln(ae)+C ...

∫ a^x · e^xdx =∫ (ae)^xdx {∵∫ a^x dx= a^xln a+C nbsp; } =(ae)^xln(ae)+C ...

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Byju's Answer

Standard XII

Physics

Definite Integrals

The value of ...

Question

The value of $\int a^{x} \cdot e^{x} d x$ is equal to, where $a > 0$ and $a \neq 1$
(where $C$ is integration constant)

\frac{(a e)^{x}}{ln (a e)} + C

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\frac{(a e)^{- x}}{ln (a e)} + C

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\frac{e^{x}}{ln (a e)} + C

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\frac{(a e)^{x}}{ln (e)} + C

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Solution

The correct option is A $\frac{(a e)^{x}}{ln (a e)} + C$
$\int a^{x} \cdot e^{x} d x = \int (a e)^{x} d x {∵ \int a^{x} d x = \frac{a^{x}}{ln a} + C} = \frac{(a e)^{x}}{ln (a e)} + C$

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The value of ∫ax⋅exdx is equal to, where a>0 and a≠1 (where C is integration constant)

The correct option is A (ae)xln(ae)+C∫ax⋅exdx=∫(ae)xdx{∵∫axdx=axlna+C}=(ae)xln(ae)+C

The value of $\int a^{x} \cdot e^{x} d x$ is equal to, where $a > 0$ and $a \neq 1$
(where $C$ is integration constant)

The correct option is A $\frac{(a e)^{x}}{ln (a e)} + C$
$\int a^{x} \cdot e^{x} d x = \int (a e)^{x} d x {∵ \int a^{x} d x = \frac{a^{x}}{ln a} + C} = \frac{(a e)^{x}}{ln (a e)} + C$