What is the integral from x to y of (2t+1) ?

The integral from x to y of (2t+1) is y-x+y^2-x^2

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integral from x to y of (2t+1)

\int_{x}^{y} (2 t + 1) d t

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

Solution steps

\int_{x}^{y} 2 t + 1 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} 1 d t + \int_{x}^{y} 2 t d t

\int_{x}^{y} 1 d t = y - x

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

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

What is the integral from x to y of (2t+1) ?
The integral from x to y of (2t+1) is y-x+y^2-x^2