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

The integral from pi/3 to (2pi)/3 of sin(x) is 1

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integral from pi/3 to (2pi)/3 of sin(x)

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

1

Solution steps

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

Use the common integral:

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

= [- cos (x)]_{\frac{π}{3}}^{\frac{2 π}{3}}

Compute the boundaries:

1

= 1

\int_{0}^{4} (8 x - 2 x^{2}) d x

\int_{0}^{4} x sin (3 x) d x

\int_{0}^{2 x} 2 x y^{3} - x d y

\int_{- 1}^{1} ∣ x ∣ sin (x) d x

\int_{0}^{\frac{π}{2}} x sin (3 x) d x

What is the integral from pi/3 to (2pi)/3 of sin(x) ?
The integral from pi/3 to (2pi)/3 of sin(x) is 1