What is the integral from 1 to 1.5 of cos((pix)/3) ?

The integral from 1 to 1.5 of cos((pix)/3) is (3(2-sqrt(3)))/(2pi)

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integral from 1 to 1.5 of cos((pix)/3)

\int_{1}^{1.5} cos (\frac{π x}{3}) d x

\frac{3 ( 2 - 3 )}{2 π}

Decimal Notation

0.12793 \dots

Solution steps

\int_{1}^{1.5} cos (\frac{π x}{3}) d x

Apply u-substitution

: \int_{\frac{π}{3}}^{1.57079 \dots} cos (u) \frac{3}{π} d u

= \int_{\frac{π}{3}}^{1.57079 \dots} cos (u) \frac{3}{π} d u

Take the constant out:

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

= \frac{3}{π} \cdot \int_{\frac{π}{3}}^{1.57079 \dots} cos (u) d u

Use the common integral:

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

= \frac{3}{π} [sin (u)]_{\frac{π}{3}}^{1.57079 \dots}

Compute the boundaries:

1 - \frac{3}{2}

= \frac{3}{π} (1 - \frac{3}{2})

Simplify

= \frac{3 ( 2 - 3 )}{2 π}

\frac{\partial}{\partial y} (2 e^{y} + 3 sin (y))

x^{2}, at x = 1

\frac{\partial}{\partial x} (\frac{1}{r ^{2}})

\int \frac{3}{e ^{5 x}} d x

f (x) = csc^{2} (x)

What is the integral from 1 to 1.5 of cos((pix)/3) ?
The integral from 1 to 1.5 of cos((pix)/3) is (3(2-sqrt(3)))/(2pi)