What is the integral from 0 to (3pi)/4 of cos(2t) ?

The integral from 0 to (3pi)/4 of cos(2t) is -1/2

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integral from 0 to (3pi)/4 of cos(2t)

\int_{0}^{\frac{3 π}{4}} cos (2 t) d t

- \frac{1}{2}

Decimal

- 0.5

Solution steps

\int_{0}^{\frac{3 π}{4}} cos (2 t) d t

Apply u-substitution

= \int_{0}^{\frac{3 π}{2}} 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_{0}^{\frac{3 π}{2}} cos (u) d u

Use the common integral:

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

= \frac{1}{2} [sin (u)]_{0}^{\frac{3 π}{2}}

Compute the boundaries:

- 1

= \frac{1}{2} (- 1)

Simplify

= - \frac{1}{2}

What is the integral from 0 to (3pi)/4 of cos(2t) ?
The integral from 0 to (3pi)/4 of cos(2t) is -1/2