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

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

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

\int_{0}^{\frac{π}{3}} 2 cos (x) d x

3

Decimal Notation

1.73205 \dots

Solution steps

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

Use the common integral:

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

= 2 [sin (x)]_{0}^{\frac{π}{3}}

Compute the boundaries:

\frac{3}{2}

= 2 \cdot \frac{3}{2}

Simplify

= 3

\int_{0}^{2} 5^{3 x} d x

\int_{0}^{2} (2 x^{3} - 2 x) d x

\int_{1}^{3} 2^{5 x} d x

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

\int_{1}^{3} 9 d x

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