What is the integral from-pi/2 to pi of 6cos(x) ?

The integral from-pi/2 to pi of 6cos(x) is 6

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integral from-pi/2 to pi of 6cos(x)

\int_{- \frac{π}{2}}^{π} 6 cos (x) d x

6

Solution steps

\int_{- \frac{π}{2}}^{π} 6 cos (x) d x

Take the constant out:

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

= 6 \cdot \int_{- \frac{π}{2}}^{π} cos (x) d x

Use the common integral:

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

= 6 [sin (x)]_{- \frac{π}{2}}^{π}

Compute the boundaries:

1

= 6 \cdot 1

Simplify

= 6

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

\int_{0}^{x} 6 x y d y

\int_{0}^{2} 8 - 2 x^{2} d x

\int_{1}^{\infty} \frac{5}{1 + x ^{2}} d x

\int_{0}^{4} e^{- 2 t} d t

What is the integral from-pi/2 to pi of 6cos(x) ?
The integral from-pi/2 to pi of 6cos(x) is 6