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

The integral from-pi/2 to pi of 2cos(x) is 2

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integral from-pi/2 to pi of 2cos(x)

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

2

Solution steps

\int_{- \frac{π}{2}}^{π} 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_{- \frac{π}{2}}^{π} cos (x) d x

Use the common integral:

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

= 2 [sin (x)]_{- \frac{π}{2}}^{π}

Compute the boundaries:

1

= 2 \cdot 1

Simplify

= 2

\int_{- 1}^{0} x^{3} 1 - x^{4} d x

\int_{- π}^{0} 2 x sin (n x) d x

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

\int_{1}^{2} \frac{x}{x ^{2} + 4} d x

\int_{- π}^{π} x sin (x) cos (n x) d x

What is the integral from-pi/2 to pi of 2cos(x) ?
The integral from-pi/2 to pi of 2cos(x) is 2