What is the integral from 0 to pi/2 of cos(x/3) ?

The integral from 0 to pi/2 of cos(x/3) is 3/2

Popular >

integral from 0 to pi/2 of cos(x/3)

\int_{0}^{\frac{π}{2}} cos (\frac{x}{3}) d x

\frac{3}{2}

Decimal

1.5

Solution steps

\int_{0}^{\frac{π}{2}} cos (\frac{x}{3}) d x

Apply u-substitution

: \int_{0}^{\frac{π}{6}} cos (u) \cdot 3 d u

= \int_{0}^{\frac{π}{6}} cos (u) \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int_{0}^{\frac{π}{6}} cos (u) d u

Use the common integral:

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

= 3 [sin (u)]_{0}^{\frac{π}{6}}

Compute the boundaries:

\frac{1}{2}

= 3 \cdot \frac{1}{2}

Simplify

= \frac{3}{2}

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

\int_{1}^{e} (4 e^{x} + 4 sin (x)) d x

\int_{- \frac{π}{4}}^{\frac{π}{4}} csc^{2} (x) d x

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

\int_{0}^{4} (3 x^{2} + 4 x + 7) d x

What is the integral from 0 to pi/2 of cos(x/3) ?
The integral from 0 to pi/2 of cos(x/3) is 3/2