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

The integral from-pi/2 to pi of 3cos(x) is 3

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

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

3

Solution steps

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

Take the constant out:

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

= 3 \cdot \int_{- \frac{π}{2}}^{π} cos (x) d x

Use the common integral:

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

= 3 [sin (x)]_{- \frac{π}{2}}^{π}

Compute the boundaries:

1

= 3 \cdot 1

Simplify

= 3

\int_{2}^{3} x e^{3 x} d x

\int_{- 1}^{1} 2 1 - x^{2} d x

\int_{0}^{1} (2 - x)^{4} d x

\int_{- 1}^{1} (x^{3} - x^{5}) d x

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

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