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Calculus · Definite-Integrals

Integrate cos(s) from -2t + x to 2t + x

\int_{- 2 t + x}^{2 t + x} \cos{\left(s \right)}\, ds

Step by step

  1. \int_{- 2 t + x}^{2 t + x} \cos{\left(s \right)}\, ds

    First find an antiderivative F, then evaluate F(b) − F(a).

  2. \int \cos{\left(s \right)}\, ds = \sin{\left(s \right)}

    Standard trigonometric antiderivative.

  3. F(2 t + x) - F(- 2 t + x) = \left(\sin{\left(2 t + x \right)}\right) - \left(- \sin{\left(2 t - x \right)}\right)

    Fundamental theorem of calculus: plug in the limits.

  4. = \sin{\left(2 t - x \right)} + \sin{\left(2 t + x \right)}

    Simplify.

Reveal the answer
\sin{\left(2 t - x \right)} + \sin{\left(2 t + x \right)}