What is the integral from-2 to 1 of (2t^2-1)^2 ?

The integral from-2 to 1 of (2t^2-1)^2 is 87/5

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integral from-2 to 1 of (2t^2-1)^2

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

\frac{87}{5}

Decimal

17.4

Solution steps

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

Expand

(2 t^{2} - 1)^{2} : 4 t^{4} - 4 t^{2} + 1

= \int_{- 2}^{1} 4 t^{4} - 4 t^{2} + 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_{- 2}^{1} 4 t^{4} d t - \int_{- 2}^{1} 4 t^{2} d t + \int_{- 2}^{1} 1 d t

\int_{- 2}^{1} 4 t^{4} d t = \frac{132}{5}

\int_{- 2}^{1} 4 t^{2} d t = 12

\int_{- 2}^{1} 1 d t = 3

= \frac{132}{5} - 12 + 3

Simplify

\frac{132}{5} - 12 + 3 : \frac{87}{5}

= \frac{87}{5}

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

\int_{0}^{1} (x^{\frac{1}{2}} - x^{2}) d x

\int_{0}^{5} 7 d x

\int_{0}^{2} \frac{1}{( x + 1 ) ^{2}} d x

\int_{\frac{1}{2}}^{1} x^{- 3} - 21 d x

What is the integral from-2 to 1 of (2t^2-1)^2 ?
The integral from-2 to 1 of (2t^2-1)^2 is 87/5