What is the integral of sin(4-x) ?

The integral of sin(4-x) is cos(4-x)+C

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integral of sin(4-x)

\int sin (4 - x) d x

cos (4 - x) + C

Solution steps

\int sin (4 - x) d x

Apply u-substitution

: \int - sin (u) d u

= \int - sin (u) d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int sin (u) d u

Use the common integral:

\int sin (u) d u = - cos (u)

= - (- cos (u))

Substitute back

u = 4 - x

= - (- cos (4 - x))

Simplify

= cos (4 - x)

Add a constant to the solution

= cos (4 - x) + C

x \to 0 lim (ln ∣ sin (x) ∣)

\frac{d}{d x} (\frac{4 x ^{3}}{3} - x + 2 e^{x})

18 y^{^{''}} - 9 y^{^{'}} - 5 y = 0

\frac{d y}{d x} + 4 x y = 0

(10, - 3), (7, 1)