Mathematics - Indefinite Integration Question with Solution | TestHub

MathematicsIndefinite IntegrationMiscellaneous formMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Consider a function $g : R \to R^{+} \cup {0}$ differentiable in its domain and satisfying

$\frac{xg ( x )}{y g ( y )} = g (\frac{x}{y})$

such that $g^{'} (1) = 2$ and $g (1) = 1$ .

$\int e^{x} (xg (x) - 6 x) d x$ is equal to:

Answer:

Solution:

$g (x) = x^{2}$

Hence, $∣ g (x) ∣ = 3$ has 2 solutions.

$\int e^{x} (x^{3} - 6 x) d x = \int e^{x} (x^{3} + 3 x^{2} - 3 x^{2} - 6 x) d x$

$= \int e^{x} (x^{3} + 3 x^{2}) d x - \int e^{x} (3 x^{2} + 6 x) d x$

$= e^{x} (x^{3} - 3 x^{2}) + C$

Stream:JEESubject:MathematicsTopic:Indefinite IntegrationSubtopic:Miscellaneous form

⏱ 2mℹ️ Source: QB

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