What is the integral of cos(10θ) ?

The integral of cos(10θ) is 1/10 sin(10θ)+C

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integral of cos(10θ)

\int cos (10 θ) d θ

\frac{1}{10} sin (10 θ) + C

Solution steps

\int cos (10 θ) d θ

Apply u-substitution

: \int cos (u) \frac{1}{10} d u

= \int cos (u) \frac{1}{10} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int cos (u) d u

Use the common integral:

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

= \frac{1}{10} sin (u)

Substitute back

u = 10 θ

= \frac{1}{10} sin (10 θ)

Add a constant to the solution

= \frac{1}{10} sin (10 θ) + C

f (x) = x, at x = 81

\frac{ln ( 1 + x ^{2} )}{x}

\frac{\partial}{\partial x} (2 y cos (x))

\int x^{3} \cdot e^{- 2 x} d x

\int_{0}^{2.5} 80 x d x