Evaluate - e sin-cos- d-

Given ∫e^sinθcosθdθ Substituting u=sinθ→ dx=1cosθdu =∫e^udu =e^u =e^sinθ+C ...

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Byju's Answer

Standard XII

Mathematics

Integration of Trigonometric Functions

Evaluate ∫ ...

Question

Evaluate $\int e^{sin θ} cos θ d θ$

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Solution

Given $\int e^{sin θ} cos θ d θ$
Substituting $u = sin θ \to d x = \frac{1}{cos θ} d u$
$= \int e^{u} d u$
$= e^{u}$
$= e^{sin θ} + C$

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Evaluate ∫esinθcosθdθ

Given ∫esinθcosθdθSubstituting u=sinθ→dx=1cosθdu=∫eudu=eu=esinθ+C

Evaluate $\int e^{sin θ} cos θ d θ$

Given $\int e^{sin θ} cos θ d θ$
Substituting $u = sin θ \to d x = \frac{1}{cos θ} d u$
$= \int e^{u} d u$
$= e^{u}$
$= e^{sin θ} + C$