What is the integral from x to y of (2t-3) ?

The integral from x to y of (2t-3) is -3y+3x+y^2-x^2

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integral from x to y of (2t-3)

\int_{x}^{y} (2 t - 3) d t

- 3 y + 3 x + y^{2} - x^{2}

Solution steps

\int_{x}^{y} 2 t - 3 d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int_{x}^{y} 3 d t + \int_{x}^{y} 2 t d t

\int_{x}^{y} 3 d t = 3 y - 3 x

\int_{x}^{y} 2 t d t = y^{2} - x^{2}

= - (3 y - 3 x) + y^{2} - x^{2}

Simplify

= - 3 y + 3 x + y^{2} - x^{2}

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What is the integral from x to y of (2t-3) ?
The integral from x to y of (2t-3) is -3y+3x+y^2-x^2