What is the integral from pi/6 to pi/3 of cos(2x) ?

The integral from pi/6 to pi/3 of cos(2x) is 0

Popular >

integral from pi/6 to pi/3 of cos(2x)

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (2 x) d x

0

Solution steps

\int_{\frac{π}{6}}^{\frac{π}{3}} cos (2 x) d x

Apply u-substitution

: \int_{\frac{π}{3}}^{\frac{2 π}{3}} cos (u) \frac{1}{2} d u

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

Use the common integral:

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

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

Compute the boundaries:

0

= \frac{1}{2} \cdot 0

Simplify

= 0

\int_{0}^{10} 2000 - 12 x^{2} d x

\int_{2}^{3} 5^{3 x} d x

\int_{0}^{x} e^{- 3 x} d x

\int_{1}^{4} y d y

\int_{0}^{2 π} 2 d t

What is the integral from pi/6 to pi/3 of cos(2x) ?
The integral from pi/6 to pi/3 of cos(2x) is 0