If e^ 3x , , 4x ,dx , = , e^ 3x , (A ,4x + B , ,4x) + c then : - Vidyadip

MCQ

If $\int {} e^{3x}\, \cos\, 4x \,dx\, = \, e^{3x}\,$ $(A \sin \,4x + B\, \cos \,4x)$ $+ c$ then :

A
$4A = 3B$
B
$2A = 3B$
✓
$3A = 4B$
D
$4B + 3A = 1$

✓

Answer

Correct option: C.

$3A = 4B$

c
Using $\int e^{a x} \cos b x \quad d x=\frac{e^{a x}}{a^{2}+b^{2}}(a \cos b x+\sin b x)$

Then

$\int e^{3 x} \cos 4 x d x=\frac{e^{3 x}}{25}(3 \cos 4 x+4 \sin 4 x)$

We get $A=\frac{4}{25}$ and $B=\frac{3}{25}$

$\therefore 3 A=4 B, 4 A+3 B=1$

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