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

The integral from 0 to pi/2 of 2cos(θ) is 2

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integral from 0 to pi/2 of 2cos(θ)

\int_{0}^{\frac{π}{2}} 2 cos (θ) d θ

2

Solution steps

\int_{0}^{\frac{π}{2}} 2 cos (θ) d θ

Take the constant out:

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

= 2 \cdot \int_{0}^{\frac{π}{2}} cos (θ) d θ

Use the common integral:

\int cos (θ) d θ = sin (θ)

= 2 [sin (θ)]_{0}^{\frac{π}{2}}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int_{0}^{4} x^{2} + 4 d x

\int_{- 8}^{0} 3 x d x

\int_{2}^{3} (8 x^{3} + 3 x^{2} + 6 x) d x

\int_{x^{4}}^{x^{6}} (2 t - 1)^{3} d t

\int_{- 1}^{2} 2 x^{2} - 2 x^{3} + 4 x d x

What is the integral from 0 to pi/2 of 2cos(θ) ?
The integral from 0 to pi/2 of 2cos(θ) is 2