What is the integral from-2 to x of (28t^2-27t) ?

The integral from-2 to x of (28t^2-27t) is (28(x^3+8))/3-27((x^2)/2-2)

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integral from-2 to x of (28t^2-27t)

\int_{- 2}^{x} (28 t^{2} - 27 t) d t

\frac{28 ( x ^{3} + 8 )}{3} - 27 (\frac{x ^{2}}{2} - 2)

Solution steps

\int_{- 2}^{x} 28 t^{2} - 27 t 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_{- 2}^{x} 28 t^{2} d t - \int_{- 2}^{x} 27 t d t

\int_{- 2}^{x} 28 t^{2} d t = \frac{28 ( x ^{3} + 8 )}{3}

\int_{- 2}^{x} 27 t d t = 27 (\frac{x ^{2}}{2} - 2)

= \frac{28 ( x ^{3} + 8 )}{3} - 27 (\frac{x ^{2}}{2} - 2)

\int_{1}^{5} (\frac{8}{x} - e^{- x}) d x

\int_{0}^{5} (2 t - 1)^{2} d t

\int_{3}^{7} (1 + x) d x

\int_{1}^{e^{2}} \frac{6 ln ( x )}{x} d x

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

What is the integral from-2 to x of (28t^2-27t) ?
The integral from-2 to x of (28t^2-27t) is (28(x^3+8))/3-27((x^2)/2-2)