What is the integral from pi to x of cos(2x) ?

The integral from pi to x of cos(2x) is 1/2 sin(2x)

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integral from pi to x of cos(2x)

\int_{π}^{x} cos (2 x) d x

\frac{1}{2} sin (2 x)

Solution steps

\int_{π}^{x} cos (2 x) d x

Apply u-substitution

: \int_{2 π}^{2 x} cos (u) \frac{1}{2} d u

= \int_{2 π}^{2 x} cos (u) \frac{1}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{2 π}^{2 x} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{2 π}^{2 x}

Compute the boundaries:

sin (2 x)

= \frac{1}{2} sin (2 x)

\int_{0}^{\frac{π}{4}} x^{2} cos (x) d x

\int_{z}^{2 - z^{2}} z d z

\int_{0}^{t} 5 d t

\int_{0}^{1} e^{- x} - e^{x} d x

\int_{0}^{1} 2 π x (x - x^{4}) d x

What is the integral from pi to x of cos(2x) ?
The integral from pi to x of cos(2x) is 1/2 sin(2x)