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}^{12} \frac{1}{36} (t (12 - t)) d t

\int_{1}^{2} 1 - (1 + x)^{- 2} d x

\int_{0}^{\frac{π}{3}} cos (3 x) d x

\int_{- 1}^{1} x 25 - x^{2} d x

\int_{2}^{6} 8 x^{3} + 3 x^{2} + 6 x + 3 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