What is the integral of-sin(x/a) ?

The integral of-sin(x/a) is acos(x/a)+C

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integral of-sin(x/a)

\int - sin (\frac{x}{a}) d x

a cos (\frac{x}{a}) + C

Solution steps

\int - sin (\frac{x}{a}) d x

Take the constant out:

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

= - \int sin (\frac{x}{a}) d x

Apply u-substitution

: \int sin (u) a d u

= - \int sin (u) a d u

Take the constant out:

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

= - a \cdot \int sin (u) d u

Use the common integral:

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

= - a (- cos (u))

Substitute back

u = \frac{x}{a}

= - a (- cos (\frac{x}{a}))

Simplify

= a cos (\frac{x}{a})

Add a constant to the solution

= a cos (\frac{x}{a}) + C

(x, y) \to (0, 0) lim (\frac{x y cos ( y )}{3 x ^{2} + y ^{2}})

7 - x^{2}

x \to 0 lim (4)

x \to 0 lim (\frac{x}{x ^{2} + x})

t \to 0 lim (e^{t})