What is the integral from 0 to pi/4 of 2cos(x) ?

The integral from 0 to pi/4 of 2cos(x) is square root of 2

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integral from 0 to pi/4 of 2cos(x)

\int_{0}^{\frac{π}{4}} 2 cos (x) d x

2

Decimal Notation

1.41421 \dots

Solution steps

\int_{0}^{\frac{π}{4}} 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}{4}} cos (x) d x

Use the common integral:

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

= 2 [sin (x)]_{0}^{\frac{π}{4}}

Compute the boundaries:

\frac{1}{2}

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

Simplify

= 2

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What is the integral from 0 to pi/4 of 2cos(x) ?
The integral from 0 to pi/4 of 2cos(x) is square root of 2