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Domain and Range of Basic Inverse Trigonometric Functions

If ∫ e3xsin 7...

Question

If $\int e^{3 x} sin 7 x d x = \frac{e^{3 x}}{a} [b sin c x + d cos c x] + C,$ then the value of $a + b + c + d$ is
$($ where $C$ is constant of integration $)$

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Solution

We know
$\int e^{a x} sin b x = \frac{e^{a x}}{a^{2} + b^{2}} [a sin b x - b cos b x] + C \Rightarrow \int e^{3 x} sin 7 x d x = \frac{e^{3 x}}{3^{2} + 7^{2}} [3 sin 7 x - 7 cos 7 x] + C ∴ a = 49 + 9 = 58, b = 3, c = 7, d = - 7$
Hence,
$a + b + c + d = 61$

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Domain and Range of Basic Inverse Trigonometric Functions

Standard XII Mathematics

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