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

The integral from 0 to pi/3 of 2sin(x) is 1

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integral from 0 to pi/3 of 2sin(x)

\int_{0}^{\frac{π}{3}} 2 sin (x) d x

1

Solution steps

\int_{0}^{\frac{π}{3}} 2 sin (x) d x

Take the constant out:

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

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

Use the common integral:

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

= 2 [- cos (x)]_{0}^{\frac{π}{3}}

Compute the boundaries:

\frac{1}{2}

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

Simplify

= 1

\int_{1}^{3} 3 x + 2 d x

\int_{0}^{4} - 6 x^{2} + 24 x d x

\int_{1}^{4} \frac{2 ln ( x )}{x} d x

\int_{0}^{2} \frac{y ^{3}}{y ^{4} + 1} d y

\int_{s}^{\infty} \frac{1}{x ^{2} + 1} d x

What is the integral from 0 to pi/3 of 2sin(x) ?
The integral from 0 to pi/3 of 2sin(x) is 1