What is the integral from 0 to x of-sin(pi*x) ?

The integral from 0 to x of-sin(pi*x) is -1/pi (-cos(pix)+1)

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integral from 0 to x of-sin(pi*x)

\int_{0}^{x} - sin (π \cdot x) d x

- \frac{1}{π} (- cos (π x) + 1)

Solution steps

\int_{0}^{x} - sin (π x) d x

Take the constant out:

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

= - \int_{0}^{x} sin (π x) d x

Apply u-substitution

: \int_{0}^{π x} sin (u) \frac{1}{π} d u

= - \int_{0}^{π x} sin (u) \frac{1}{π} d u

Take the constant out:

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

= - \frac{1}{π} \cdot \int_{0}^{π x} sin (u) d u

Use the common integral:

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

= - \frac{1}{π} [- cos (u)]_{0}^{π x}

Compute the boundaries:

- cos (π x) + 1

= - \frac{1}{π} (- cos (π x) + 1)

\int_{0}^{1} - 2 sin^{2} (2 - 2 t) d t

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

\int_{0}^{1} x y e^{y^{2} x} d y

\int_{0}^{0.5} C x d x

\int_{0}^{7} x x + 2 d x

What is the integral from 0 to x of-sin(pi*x) ?
The integral from 0 to x of-sin(pi*x) is -1/pi (-cos(pix)+1)